{"id":10968,"date":"2022-10-30T16:08:45","date_gmt":"2022-10-30T07:08:45","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=10968"},"modified":"2022-11-04T11:27:31","modified_gmt":"2022-11-04T02:27:31","slug":"binomial-theorem","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/binomial-theorem.html","title":{"rendered":"\u4e8c\u9805\u5b9a\u7406\uff1a\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3068\u591a\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u30fb\u516c\u5f0f"},"content":{"rendered":"\n<p>\u6570\u5b66\u3067\u5b66\u3076\u5185\u5bb9\u306b\u4e8c\u9805\u5b9a\u7406\u304c\u3042\u308a\u307e\u3059\u3002\\((a+b)^n\\)\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u3001\u4fc2\u6570\u3092\u8abf\u3079\u305f\u3044\u3068\u304d\u306b\u5f79\u306b\u7acb\u3064\u306e\u304c\u4e8c\u9805\u5b9a\u7406\u3067\u3059\u3002<\/p>\n<p>\u4e8c\u9805\u5b9a\u7406\u3067\u306f\u3001\u7d44\u307f\u5408\u308f\u305b\uff08\\(_nC_r\\)\uff09\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305d\u3053\u3067\u4e8c\u9805\u5b9a\u7406\u306e\u8003\u3048\u65b9\u3092\u5b66\u3073\u3001\u306a\u305c\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3067\u7d44\u307f\u5408\u308f\u305b\u3092\u4f7f\u3046\u306e\u304b\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u308c\u306b\u52a0\u3048\u3066\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u8a3c\u660e\u3092\u3059\u308c\u3070\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u3088\u308a\u6df1\u304f\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u4e8c\u9805\u5b9a\u7406\u3068\u95a2\u4fc2\u3042\u308b\u8a08\u7b97\u306b\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u304c\u3042\u308a\u307e\u3059\u3002\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3092\u5229\u7528\u3057\u3066\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u3092\u3057\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u307e\u305f\u4e8c\u9805\u5b9a\u7406\u306e\u767a\u5c55\u554f\u984c\u306b\u591a\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u304c\u3042\u308a\u307e\u3059\u3002\u591a\u9805\u5b9a\u7406\u306b\u3064\u3044\u3066\u3082\u3001\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4e8c\u9805\u5b9a\u7406\u3067\u306f\u3069\u306e\u3088\u3046\u306a\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e8c\u9805\u5b9a\u7406\u3060\u3051\u3067\u306a\u304f\u3001\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3084\u591a\u9805\u5b9a\u7406\u3092\u542b\u3081\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3068\u8a08\u7b97\u65b9\u6cd5<\/h2>\n<p>\u6587\u7ae0\u3092\u8aad\u3080\u3053\u3068\u3067\u4e8c\u9805\u5b9a\u7406\u3092\u7406\u89e3\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5177\u4f53\u4f8b\u3092\u7528\u3044\u3066\u4e8c\u9805\u5b9a\u7406\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u3001\u4f8b\u3068\u3057\u3066\\((a+b)^2=(a+b)(a+b)\\)\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\u591a\u9805\u5f0f\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u914d\u6cd5\u5247\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/10\/djwk1-1.jpg\" alt=\"\" width=\"347\" height=\"152\" class=\"aligncenter size-full wp-image-10970\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((a+b)^2=a^2+2ab+b^2\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u8a08\u7b97\u904e\u7a0b\u3092\u3088\u308a\u8a73\u7d30\u306b\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<span style=\"color: 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loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/10\/djwk2.jpg\" alt=\"\" width=\"600\" height=\"330\" class=\"aligncenter size-full wp-image-10971\" 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loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/10\/djwk3.jpg\" alt=\"\" width=\"600\" height=\"91\" class=\"aligncenter size-full wp-image-10972\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\\(a^{n-r}b^r\\)\u306e\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u304b\u3063\u3053\u306e\u4e2d\u304b\u3089\\(b\\)\u3092\\(r\\)\u56de\u3001\u9078\u3079\u3070\u3044\u3044\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(_nC_r\\)\uff08\u307e\u305f\u306f\\(_nC_{n-r}\\)\uff09\u3092\u8a08\u7b97\u3059\u308c\u3070\u9805\u306e\u4fc2\u6570\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u305d\u308c\u305e\u308c\u306e\u9805\u3068\u4fc2\u6570\u3092\u304b\u3051\u305f\u5f8c\u3001\u3059\u3079\u3066\u8db3\u3059\u3068\u5c55\u958b\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u5148\u307b\u3069\u306e\u516c\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002\u8a3c\u660e\u306e\u65b9\u6cd5\u306f\u3044\u304f\u3064\u304b\u5b58\u5728\u3059\u308b\u3082\u306e\u306e\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u8003\u3048\u65b9\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u306a\u305c\u5148\u307b\u3069\u306e\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3064\u306e\u304b\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u4e8c\u9805\u5b9a\u7406\u306e\u7df4\u7fd2\u554f\u984c<\/strong><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\((x-2)^5\\)\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u3001\\(x^3\\)\u306e\u4fc2\u6570\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\((x-2)^5\\)\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u3001\u304b\u3063\u3053\u306e\u6570\u306f5\u500b\u3067\u3059\u3002\u307e\u305f\\(x\\)\u30923\u56de\uff08\u307e\u305f\u306f-2\u30922\u56de\uff09\u9078\u3076\u3053\u3068\u306b\u3088\u308a\u3001\\(x^3\\)\u3092\u542b\u3080\u9805\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(_5C_2x^3(-2)^2=40x^3\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x^3\\)\u306e\u4fc2\u6570\u306f40\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3068\u4e8c\u9805\u5b9a\u7406\u306e\u95a2\u4fc2<\/h3>\n<p>\u306a\u304a\u3001\u4e8c\u9805\u5b9a\u7406\u3068\u95a2\u4fc2\u306e\u6df1\u3044\u6982\u5ff5\u306b\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u304c\u3042\u308a\u307e\u3059\u3002\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3067\u306f\u3001\u9802\u70b9\u30921\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u4e09\u89d2\u5f62\u3092\u4f5c\u308b\u3088\u3046\u306b\u5de6\u53f3\u306e\u6570\u3092\u8db3\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u4e09\u89d2\u5f62\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/10\/djwk4-1.jpg\" alt=\"\" width=\"448\" height=\"353\" class=\"aligncenter size-full wp-image-10973\" \/><\/p>\n<p>\u3053\u308c\u304c\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3067\u3059\u3002<span style=\"color: #0000ff;\">\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\u6570\u5b57\u306f\u4e8c\u9805\u5b9a\u7406\u306e\u4fc2\u6570\u306b\u76f8\u5f53\u3057\u3066\u3044\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/10\/djwk5-1.jpg\" alt=\"\" width=\"700\" height=\"150\" class=\"aligncenter size-full wp-image-10974\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u4e8c\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3092\u5229\u7528\u3057\u3066\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3069\u3061\u3089\u306e\u65b9\u6cd5\u3067\u3042\u3063\u3066\u3082\u6b63\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u53ef\u80fd\u306a\u306e\u3067\u3059\u3002<\/p>\n<p>\u305f\u3060\u7d2f\u4e57\u306e\u6570\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3092\u5229\u7528\u3057\u3066\u7b54\u3048\u3092\u5f97\u308b\u306e\u306f\u73fe\u5b9f\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u5834\u5408\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u591a\u9805\u5b9a\u7406\u306e\u5c55\u958b\u5f0f\u306e\u8003\u3048\u65b9<\/h2>\n<p>\u4e8c\u9805\u5b9a\u7406\u306e\u767a\u5c55\u554f\u984c\u3068\u3057\u3066\u591a\u9805\u5b9a\u7406\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3068\u3057\u3066\u3001\u4e09\u9805\u306e\u5f0f\u3092\u5c55\u958b\u3059\u308b\u5834\u5408\u306e\u4fc2\u6570\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u5f0f\u3092\u5c55\u958b\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\((a+b+c)^n\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u306e\u5834\u5408\u306e\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u8003\u3048\u65b9\u306f\u5148\u307b\u3069\u3068\u540c\u3058\u3067\u3042\u308a\u3001\u304b\u3063\u3053\u306e\u6570\u306b\u7740\u76ee\u3057\u307e\u3057\u3087\u3046\u3002\\((a+b+c)^n\\)\u306b\u306f\u3001\u304b\u3063\u3053\u304c\\(n\\)\u500b\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/10\/djwk6.jpg\" alt=\"\" width=\"700\" height=\"75\" class=\"aligncenter size-full wp-image-10976\" \/><\/p>\n<p>\u3053\u306e\u3068\u304d<span style=\"color: #0000ff;\">\u300c\\(a^pb^qc^r\\)\u3092\u542b\u3080\u9805\u3068\u3044\u3046\u306e\u306f\u3001\\(n\\)\u500b\u5b58\u5728\u3059\u308b\u304b\u3063\u3053\u306e\u4e2d\u304b\u3089\\(a\\)\u3092\\(p\\)\u56de\u3001\\(b\\)\u3092\\(q\\)\u56de\u3001\\(c\\)\u3092\\(r\\)\u56de\u9078\u3076\u9806\u5217\u3067\u3042\u308b\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u304c\\(a^pb^qc^r\\)\u306e\u4fc2\u6570\u3092\u5f97\u308b\u516c\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{n!}{p!q!r!}\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\\((a+b+c)^n\\)\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u822c\u9805\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{n!}{p!q!r!}a^pb^qc^r\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u516c\u5f0f\u3092\u6697\u8a18\u3057\u3066\u3082\u610f\u5473\u304c\u306a\u304f\u3001\u306a\u305c\u3053\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u8a08\u7b97\u3067\u304d\u308b\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308c\u3070\u3001\u516c\u5f0f\u3092\u899a\u3048\u306a\u304f\u3066\u3082\u516c\u5f0f\u306e\u5c0e\u51fa\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u5f53\u7136\u306a\u304c\u3089\u3001<span style=\"color: #ff0000;\">\u304b\u3063\u3053\u306e\u6570\u306f\\(n\\)\u500b\u3067\u3042\u308b\u305f\u3081\u3001\\(p+q+r=n\\)\u3092\u6e80\u305f\u3057\u307e\u3059\u3002<\/span>\u307e\u305f\\(p\u22670\\)\u3001\\(q\u22670\\)\u3001\\(r\u22670\\)\u3067\u3059\u3002<\/p>\n<p>\u203b\\(0!=1\\)\u3068\u5b9a\u3081\u307e\u3059\u3002<\/p>\n<h3>\u5206\u6570\u3092\u542b\u3080\u5834\u5408\u306e\u591a\u9805\u5c55\u958b\u5f0f\u306e\u8a08\u7b97\uff1a\u5b9a\u6570\u9805\u3092\u6c42\u3081\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u591a\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(\\left(x+\\displaystyle\\frac{1}{x}-1\\right)^8\\)\u306e\u5c55\u958b\u5f0f\u306b\u3064\u3044\u3066\u3001\u5b9a\u6570\u9805\uff08\u6b21\u6570\u304c0\u306b\u306a\u308b\u9805\uff09\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\\(\\left(x+\\displaystyle\\frac{1}{x}-1\\right)^8\\)\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{8!}{p!q!r!}x^p\\left(\\displaystyle\\frac{1}{x}\\right)^q(-1)^r\\)\\(=\\displaystyle\\frac{8!}{p!q!r!}x^{p-q}(-1)^r\\)<\/p>\n<p>\u306a\u304a\u3001\\(p,q,r\\)\u306f\\(p+q+r=8\\)\u3092\u6e80\u305f\u3059\u6b63\u306e\u6574\u6570\u3067\u3059\u3002<\/p>\n<p>\u5148\u307b\u3069\u306e\u5f0f\u3092\u78ba\u8a8d\u3057\u3066\u308f\u304b\u308b\u901a\u308a\u3001\u9805\u306e\u6b21\u6570\u304c\u30bc\u30ed\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u3001\\(p-q=0\\)\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(p=q\\)\u3067\u3059\u3002\\(p=q\\)\u3068\\(p+q+r=8\\)\u3092\u6e80\u305f\u3059\u6b63\u306e\u6574\u6570\\(p,q,r\\)\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(0,0,8\\)<\/li>\n<li>\\(1,1,6\\)<\/li>\n<li>\\(2,2,4\\)<\/li>\n<li>\\(3,3,2\\)<\/li>\n<li>\\(4,4,0\\)<\/li>\n<\/ul>\n<p>\u3053\u306e4\u3064\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u6b21\u6570\u304c0\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u591a\u9805\u5b9a\u7406\u306e\u5c55\u958b\u5f0f\u3092\u5229\u7528\u3057\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u3066\u5b9a\u6570\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{8!}{8!}(-1)^8+\\displaystyle\\frac{8!}{6!}(-1)^6+\\displaystyle\\frac{8!}{2!2!4!}(-1)^4\\)\\(+\\displaystyle\\frac{8!}{3!3!2!}(-1)^2\\)\\(+\\displaystyle\\frac{8!}{4!4!}(-1)^0\\)<\/p>\n<p>\\(=1+56+420+560+70\\)<\/p>\n<p>\\(=1107\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5b9a\u6570\u9805\u306f1107\u3068\u8a08\u7b97\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>n\u30b1\u30bf\u306e\u6570\u3092\u5f97\u308b\u4e8c\u9805\u5b9a\u7406\u306e\u5229\u7528<\/h3>\n<p>\u6b21\u306b\u3001\u4e8c\u9805\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066n\u30b1\u30bf\u306e\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\u7279\u5b9a\u306e\u30b1\u30bf\u6570\u3092\u5f97\u308b\u306e\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>101<sup>100<\/sup>\u306b\u3064\u3044\u3066\u3001\u4e0b5\u30b1\u30bf\u306e\u6570\u5b57\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5b9f\u969b\u306b\u3053\u306e\u8a08\u7b97\u3092\u3059\u308b\u306e\u306f\u73fe\u5b9f\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u4e8c\u9805\u5b9a\u7406\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u306e\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3059\u3002<\/p>\n<p>\\(101^{100}=(1+100)^{100}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\((a+b)^{100}\\)\u306e\u5f62\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u305d\u3053\u3067\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\((1+100)^{100}\\)<\/p>\n<p>\\(=1+_{100}C_1\u00d7100+_{100}C_2\u00d7100^2+_{100}C_3\u00d7100^3\u00d7N\\)<\/p>\n<p>\u203b\\(N\\)\u306f\u81ea\u7136\u6570<\/p>\n<p>\\(N\\)\u306e\u5024\u306f\u4e0d\u660e\u3067\u3059\u3002\u305f\u3060\u4e0b5\u30b1\u30bf\u306e\u6570\u5b57\u304c\u308f\u304b\u308c\u3070\u3044\u3044\u305f\u3081\u3001\\(N\\)\u306e\u5024\u304c\u4e0d\u660e\u3067\u3042\u3063\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u307e\u305f\u5148\u307b\u3069\u306e\u5f0f\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\u4e8c\u9805\u5b9a\u7406\u306b\u3088\u3063\u3066100\u306e\u7d2f\u4e57\u3092\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u3001\u7b2c4\u9805\u3067\u306f\u7b54\u3048\u306b100<sup>3<\/sup>\u3092\u304b\u3051\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u5fc5\u305a\u4e0b5\u30b1\u30bf\u3088\u308a\u3082\u6570\u5b57\u304c\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7b2c4\u9805\u3084\u7b2c5\u9805\u3092\u8a08\u7b97\u3057\u3066\u3082\u4e0b5\u30b1\u30bf\u306e\u6570\u5b57\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u90e8\u5206\uff08\u7b2c1\u9805\u304b\u3089\u7b2c3\u9805\u307e\u3067\uff09\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(1+_{100}C_1\u00d7100+_{100}C_2\u00d7100^2\\)<\/p>\n<p>\\(=1+10000+495\u00d710^5\\)<\/p>\n<p>\\(=49510001\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4e0b5\u30b1\u30bf\u306f10001\u3067\u3042\u308b\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u4e8c\u9805\u5b9a\u7406\u3068\u591a\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u3082\u3064\u610f\u5473\u3092\u5b66\u3076<\/h2>\n<p>\u4e8c\u9805\u5b9a\u7406\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u591a\u304f\u306e\u4eba\u306f\u516c\u5f0f\u3092\u6697\u8a18\u3057\u307e\u3059\u3002\u305f\u3060\u3001\u516c\u5f0f\u306e\u6697\u8a18\u3067\u306f\u610f\u5473\u304c\u306a\u304f\u3001\u516c\u5f0f\u3092\u5fd8\u308c\u305f\u3089\u8a08\u7b97\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u3082\u3064\u610f\u5473\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308c\u3070\u3001\u3044\u3064\u3067\u3082\u516c\u5f0f\u3092\u4f5c\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u306f\u591a\u9805\u5b9a\u7406\u3082\u540c\u69d8\u3067\u3059\u3002\u591a\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3067\u306f\u3001\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u306a\u304f\u3001\u9806\u5217\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u8003\u3048\u65b9\u306f\u4e8c\u9805\u5b9a\u7406\u3068\u540c\u3058\u3067\u3042\u308a\u3001\u516c\u5f0f\u304c\u3082\u3064\u610f\u5473\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3092\u5229\u7528\u3057\u3066\u4e8c\u9805\u5b9a\u7406\u306e\u8a08\u7b97\u3092\u3057\u3066\u3082\u3044\u3044\u3067\u3059\u3002\u7d2f\u4e57\u306e\u6570\u304c\u5c0f\u3055\u3044\u5834\u5408\u3001\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u304c\u6709\u52b9\u3067\u3059\u3002<\/p>\n<p>\u516c\u5f0f\u3092\u6697\u8a18\u3057\u3066\u306f\u3044\u3051\u306a\u3044\u6570\u5b66\u306e\u5185\u5bb9\u304c\u4e8c\u9805\u5b9a\u7406\u3068\u591a\u9805\u5b9a\u7406\u3067\u3059\u3002\u516c\u5f0f\u306e\u610f\u5473\u3092\u5b66\u3073\u3001\u7d44\u307f\u5408\u308f\u305b\u3068\u9806\u5217\u3092\u7528\u3044\u3066\u7b54\u3048\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u5b66\u3067\u5b66\u3076\u5185\u5bb9\u306b\u4e8c\u9805\u5b9a\u7406\u304c\u3042\u308a\u307e\u3059\u3002\\((a+b)^n\\)\u3092\u5c55\u958b\u3059\u308b\u3068\u304d\u3001\u4fc2\u6570\u3092\u8abf\u3079\u305f\u3044\u3068\u304d\u306b\u5f79\u306b\u7acb\u3064\u306e\u304c\u4e8c\u9805\u5b9a\u7406\u3067\u3059\u3002 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