{"id":86,"date":"2023-07-17T12:15:31","date_gmt":"2023-07-17T12:15:31","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e9%98%b6%e4%b9%98%e8%ae%a1%e7%ae%97%e5%99%a8\/"},"modified":"2023-07-17T12:15:31","modified_gmt":"2023-07-17T12:15:31","slug":"%e9%98%b6%e4%b9%98%e8%ae%a1%e7%ae%97%e5%99%a8","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e9%98%b6%e4%b9%98%e8%ae%a1%e7%ae%97%e5%99%a8\/","title":{"rendered":"\u5982\u4f55\u5728\u8ba1\u7b97\u5668\u4e2d\u4f7f\u7528\u9636\u4e58\u51fd\u6570\uff1f"},"content":{"rendered":"<p>\u9636\u4e58\u662f\u4e00\u4e2a<strong>\u975e\u5e38\u5bb9\u6613\u8ba1\u7b97\u7684\u6570\u5b66\u51fd\u6570<\/strong>\uff0c\u7528\u611f\u53f9\u53f7\u8868\u793a\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u6b64\u6570\u5b66\u8fd0\u7b97\u7684\u8bed\u6cd5\u662f\u4e00\u4e2a\u6574\u6570\u540e\u8ddf\u4e00\u4e2a\u611f\u53f9\u53f7\u3002\u4f46\u662f\uff0c\u8ba9\u5f88\u591a\u540c\u5b66\u7591\u60d1\u7684\u662f\uff0c\u9636\u4e58\u5230\u5e95\u6709\u4ec0\u4e48\u7528\uff0c\u53c8\u5982\u4f55\u5199\u5728<a href=\"https:\/\/mathority.org\/cn\" target=\"_blank\" rel=\"noreferrer noopener\">\u79d1\u5b66\u8ba1\u7b97\u5668<\/a>\u4e0a\u5462\uff1f\u56e0\u6b64\uff0c\u5728\u672c\u6587\u4e2d\u6211\u4eec\u5c06\u89e3\u51b3\u8fd9\u4e24\u4e2a\u95ee\u9898\uff0c\u60a8\u4e5f\u53ef\u4ee5\u5c1d\u8bd5\u6211\u4eec\u7684\u5728\u7ebf\u9636\u4e58\u8ba1\u7b97\u5668\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"calculadora-de-factoriales-online\"><span id=\"Calculadora_de_factoriales_online\">\u5728\u7ebf\u56e0\u5b50\u8ba1\u7b97\u5668<\/span><\/h2>\n<p>\u8981\u4f7f\u7528\u6b64\u5728\u7ebf\u9636\u4e58\u8ba1\u7b97\u5668\uff0c\u53ea\u9700\u8f93\u5165\u521d\u59cb\u6570\u5b57\u5e76\u5355\u51fb\u201c\u8ba1\u7b97\u201d\uff0c\u7ed3\u679c\u5c06\u663e\u793a\u5728\u201c\u9636\u4e58\u201d\u6846\u4e2d\u3002<\/p>\n<p><title>\u9636\u4e58\u8ba1\u7b97\u5668<\/title><script language=\"javascript\"><\/p>\n<p>function factorial (){\n\tvar factorial = 1;<\/p>\n<p>        for (var i=1; i <= document.getElementById ('n').value; i++){\n            factorial *= i;\n        }\n \n        document.getElementById ('resultado').value = factorial;\n}\n \n<\/script><\/p>\n<form onsubmit=\"javascript: factorial ();return (false);\">\u53f7\u7801\uff1a<input type=\"text\" name=\"n\" id=\"n\"><\/p>\n<p>\u9636\u4e58\uff1a <input type=\"text\" name=\"resultado\" id=\"resultado\" readonly=\"readonly\"><\/p>\n<p><input type=\"submit\" value=\"\u8ba1\u7b97\"><\/p>\n<\/form>\n<h2 class=\"wp-block-heading\" id=\"que-es-un-factorial\"><span id=\"Que_es_un_factorial\">\u4ec0\u4e48\u662f\u9636\u4e58\uff1f<\/span><\/h2>\n<p><strong>\u6570\u5b57\u7684\u9636\u4e58<\/strong>\u662f\u4ece 1 \u5230\u8be5\u6570\u5b57\u7684\u6240\u6709<a href=\"https:\/\/mathority.org\/cn\/\u81ea\u7136\u6570\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6b63\u6574\u6570<\/a>\u7684\u4e58\u79ef\u3002\u56e0\u6b64\uff0c\u5982\u679c\u4f60\u60f3\u77e5\u90534\u7684\u9636\u4e58\uff0c\u90a3\u4e48\u4f60\u9700\u8981\u8fdb\u884c\u4ee5\u4e0b\u8ba1\u7b97\uff1a <strong>4\uff01 = 1 x 2 x 3 x 4 = 24<\/strong> \u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u5bb9\u6613\u7406\u89e3\u7684\u6982\u5ff5\uff0c\u552f\u4e00\u590d\u6742\u7684\u662f\u5982\u4f55\u5c06\u5176\u5e94\u7528\u5230\u6982\u7387\u4e16\u754c\u4e2d\u3002\u4f46\u662f\uff0c\u5c31\u6570\u5b66\u8ba1\u7b97\u800c\u8a00\uff0c\u60a8\u53ea\u9700\u5728\u8fdb\u884c\u4e58\u6cd5\u8fd0\u7b97\u65f6\u5c3d\u91cf\u4e0d\u8981\u72af\u9519\u5373\u53ef\uff0c\u4ec5\u6b64\u800c\u5df2\uff01<\/p>\n<p>\u9636\u4e58\u6570\u7684\u91cd\u8981\u6027\u5728\u4e8e<strong>\u7ec4\u5408\u6570\u5b66\u548c\u6982\u7387<\/strong>\u6570\u5b66\u9886\u57df\u3002\u4f8b\u5982\uff0c\u5b83\u4eec\u7ecf\u5e38\u7528\u4e8e\u6d89\u53ca\u5361\u7247\u6216\u9ab0\u5b50\u7684\u5178\u578b\u6570\u5b66\u7ec3\u4e60\u4e2d\uff0c\u5176\u4e2d\u60a8\u5fc5\u987b\u5bf9\u4e0d\u540c\u7684\u53ef\u80fd\u987a\u5e8f\u5e8f\u5217\u8fdb\u884c\u6392\u5e8f\u6216\u8ba1\u6570\u3002\u8fd9\u4e2a\u6982\u5ff5\u79f0\u4e3a<strong>\u6392\u5217<\/strong>\uff0c\u4e0e\u9636\u4e58\u7684\u4f7f\u7528\u5bc6\u5207\u76f8\u5173\u3002\u7a0d\u540e\u6211\u4eec\u4f1a\u7ee7\u7eed\u8bb2\u9636\u4e58\u6570\u7684\u5e94\u7528\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"propiedades-de-los-factoriales\">\u9636\u4e58\u7684\u6027\u8d28<\/h3>\n<p>\u5728\u4e0b\u9762\u7684\u5217\u8868\u4e2d\uff0c\u60a8\u53ef\u4ee5\u627e\u5230\u9636\u4e58\u6570\u7684\u4e09\u4e2a\u4e3b\u8981\u5c5e\u6027\uff0c\u5b83\u4eec\u90fd\u975e\u5e38\u76f4\u89c2\uff1a<\/p>\n<ul>\n<li>\u5982\u679c n &gt; m\uff0c\u5219 n! &gt; \u6211\uff01 \u2192 4 &gt; 3\uff0c\u56e0\u6b64 4\uff01 &gt; 3\uff01<\/li>\n<li>\u5982\u679c n &gt; m\uff0c\u5219 n! = nx (n - 1) ... (m + 1) xm\uff01 \u2192 5\uff01 = 3\uff01 4x5<\/li>\n<li>\u5982\u679c n=! 1\u3001\u90a3\u5c31\u4e0d\u884c\uff01 &lt; ((n+1)\/2)\u00b2 \u2192 2! &lt; ((2+1)\/2)\u00b2<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\" id=\"ejemplos-de-calculo-de-un-factorial\">\u8ba1\u7b97\u9636\u4e58\u7684\u793a\u4f8b<\/h3>\n<p>\u4e0b\u9762\uff0c\u60a8\u5c06\u627e\u5230\u4e00\u4e2a\u4ece 1 \u5230 10 \u7684\u9636\u4e58\u8868\uff0c\u4ee5\u4fbf\u5b8c\u6210\u5bf9\u8ba1\u7b97\u673a\u5236\u7684\u7406\u89e3\uff1a<\/p>\n<figure class=\"wp-block-table\">\n<table class=\"has-fixed-layout\">\n<tbody>\n<tr>\n<td>\u4ef7\u503c<\/td>\n<td>\u76f8\u5e94\u7684\u9636\u4e58<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td> 1<\/td>\n<\/tr>\n<tr>\n<td> 2<\/td>\n<td> 1\u00d72=2<\/td>\n<\/tr>\n<tr>\n<td> 3<\/td>\n<td> 1\u00d72\u00d73=6<\/td>\n<\/tr>\n<tr>\n<td> 4<\/td>\n<td> 1 \u00d7 2 \u00d7 3 \u00d7 4 = 24<\/td>\n<\/tr>\n<tr>\n<td> 5<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75=120<\/td>\n<\/tr>\n<tr>\n<td> 6<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\u00d76=720<\/td>\n<\/tr>\n<tr>\n<td> 7<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\u00d76\u00d77=5040<\/td>\n<\/tr>\n<tr>\n<td> 8<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\u00d76\u00d77\u00d78=40320<\/td>\n<\/tr>\n<tr>\n<td> 9<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\u00d76\u00d77\u00d78\u00d79=362880<\/td>\n<\/tr>\n<tr>\n<td>\u5341<\/td>\n<td>1\u00d72\u00d73\u00d74\u00d75\u00d76\u00d77\u00d78\u00d79\u00d710 = 3628800<\/td>\n<\/tr>\n<\/tbody>\n<\/table><figcaption> 1 \u5230 10 \u7684\u9636\u4e58\u8868<\/figcaption><\/figure>\n<h3 class=\"wp-block-heading\" id=\"factorial-de-un-numero-negativo\">\u8d1f\u6570\u7684\u9636\u4e58<\/h3>\n<p>\u6709\u65f6\u6709\u4eba\u8bf4\uff0c\u5728\u6570\u5b66\u4e0a\u4e0d\u53ef\u80fd\u5bf9\u8d1f\u6570\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u56e0\u6b64\u65e0\u6cd5\u8ba1\u7b97\u8d1f\u6570\u7684\u9636\u4e58\u3002\u8fd9\u901a\u5e38\u5728\u5e74\u7ea7\u8fdb\u884c\u6559\u6388\uff0c\u4ee5\u907f\u514d\u6df7\u6dc6\u3002\u4f46\u662f\uff0c\u5f53\u4f60\u8fbe\u5230\u4e00\u5b9a\u7684\u6570\u5b66\u6c34\u5e73\u5e76\u5b66\u4e60\u4e86<strong>\u6b27\u62c9\u7684\u201c\u4f3d\u739b\u51fd\u6570\u201d<\/strong>\u65f6\uff0c\u4f60\u5c31\u4f1a\u660e\u767d\u4f60\u53ef\u4ee5\u8ba1\u7b97\u4efb\u4f55\u8d1f\u6570\u3001\u5c0f\u6570\u548c\u5206\u6570\u7684\u9636\u4e58\u3002\u8be5\u51fd\u6570\u7531\u4ee5\u4e0b\u79ef\u5206\u5b9a\u4e49\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"194\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-gamma-deuler.webp\" data-src=\"\" alt=\"\u6b27\u62c9\u4f3d\u739b\u51fd\u6570\" class=\"wp-image-4665 lazyload\" srcset=\"\" sizes=\"auto, \"><figcaption>\u6b27\u62c9\u4f3d\u739b\u51fd\u6570<\/figcaption><\/figure>\n<\/div>\n<p>\u548c\u5f80\u5e38\u4e00\u6837\uff0c\u65b9\u7a0b<strong>n! = \u0413(n+1)<\/strong> \uff0c\u5219\u4efb\u4f55\u7c7b\u578b\u7684\u9636\u4e58\u90fd\u53ef\u4ee5\u7528 Gamma \u51fd\u6570\u627e\u5230\u3002\u60a8\u53ea\u9700\u8bb0\u4f4f\uff0c\u8981\u8ba1\u7b97 0.25 \u7684\u9636\u4e58\uff0c\u60a8\u5b9e\u9645\u4e0a\u9700\u8981\u8ba1\u7b97 \u0393(1.25) \u7684\u503c\u3002\u4ece\u90a3\u65f6\u8d77\uff0c0.25\uff01 = \u0413(0.25 + 1) = \u0413(1.25)\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"factorial-de-0\"> 0 \u7684\u9636\u4e58<\/h3>\n<p>\u96f6\u7684\u9636\u4e58\u6709\u70b9\u4e0d\u540c\uff0c\u56e0\u4e3a<strong>0! = 1<\/strong> \u3002\u8fd9\u53ef\u80fd\u4f1a\u8ba9\u6211\u4eec\u6709\u70b9\u60ca\u8bb6\uff0c\u4f46\u662f\u4e00\u65e6\u6211\u4eec\u89e3\u91ca\u4e86\u539f\u56e0\uff0c\u6211\u4eec\u5c31\u4f1a\u5f88\u597d\u7406\u89e3\u3002\u90a3\u4e48\uff0c\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u4e4b\u524d\u8ba8\u8bba\u8fc7\u7684\u9636\u4e58\u7684\u5b9a\u4e49\uff1a\u201c\u6570\u5b57\u7684\u9636\u4e58\u662f\u4ece 1 \u5230\u8be5\u6570\u5b57\u7684\u6240\u6709\u6b63\u6574\u6570\u7684\u4e58\u79ef\u3002\u201d\u597d\u5427\uff0c\u8bdd\u867d\u5982\u6b64\uff0c\u6211\u4eec\u5c06\u770b\u5230\u4e00\u7cfb\u5217\u516c\u5f0f\uff0c\u5b83\u4eec\u5c06\u5411\u6211\u4eec\u5c55\u793a<strong>0\uff01 = 1<\/strong> :<\/p>\n<p> 2\uff01 = 3!\/3 = 6\/3 = 2<\/p>\n<p> 1\uff01 = 2!\/2 = 2\/2 = 1<\/p>\n<p> 0\uff01 = 1!\/1 = 1\/1 = 1<\/p>\n<h2 class=\"wp-block-heading\" id=\"como-calcular-un-factorial-en-la-calculadora-cientifica\"><span id=\"Como_calcular_un_factorial_en_la_calculadora_cientifica\">\u5982\u4f55\u5728\u79d1\u5b66\u8ba1\u7b97\u5668\u4e0a\u8ba1\u7b97\u9636\u4e58\uff1f<\/span><\/h2>\n<p>\u5f53\u60a8\u9700\u8981\u8ba1\u7b97\u5927\u6570\u7684\u9636\u4e58\u65f6\uff0c\u5f3a\u70c8\u5efa\u8bae\u4f7f\u7528<strong>\u8ba1\u7b97\u5668\u7684\u9636\u4e58\u51fd\u6570<\/strong>\u3002\u5426\u5219\u4f60\u4f1a\u75af\u72c2\u5730\u89e3\u51b3\u8fd9\u4e48\u591a\u4e58\u6cd5\u3002\u8fd9\u6837\uff0c\u60a8\u4e0d\u4ec5\u53ef\u4ee5\u8282\u7701\u65f6\u95f4\uff0c\u8fd8\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u8ba1\u7b97\u4e0e\u8ba1\u7b97\u5668\u7684\u6982\u7387\u51fd\u6570\u6df7\u5408\u5728\u4e00\u8d77\uff0c\u4ece\u800c\u66f4\u597d\u5730\u4ea4\u7ec7\u60a8\u7684\u6570\u5b66\u8ba1\u7b97\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u89e3\u51b3\u6b64\u7c7b\u8ba1\u7b97\uff0c\u60a8\u9700\u8981\u5728\u8ba1\u7b97\u5668\u4e2d\u627e\u5230\u9636\u4e58\u7b26\u53f7<strong>n!, x!\u4efb\u4f55\u4e00\u4e2a\uff01<\/strong> \u3002\u5f53\u7136\uff0c\u60a8\u5fc5\u987b\u5c0f\u5fc3\u5730\u4ee5\u6b63\u786e\u7684\u987a\u5e8f\u7f16\u5199\u8fd0\u7b97\uff1a\u6570\u5b57+\u9636\u4e58\u7b26\u53f7\u3002\u53e6\u5916\uff0c\u60a8\u5fc5\u987b\u8003\u8651\u5230\u5b83\u662f\u4e00\u4e2a\u5e26\u6709\u9636\u4e58\u7684\u8ba1\u7b97\u5668\uff0c\u56e0\u4e3a\u5982\u679c\u5b83\u4e0d\u5305\u542b\u9636\u4e58\u51fd\u6570\uff0c\u60a8\u5c06\u65e0\u6cd5\u89e3\u51b3\u8fd9\u79cd\u98ce\u683c\u7684\u8ba1\u7b97\u3002\u4f46\u5e78\u8fd0\u7684\u662f\uff0c\u5982\u4eca\u51e0\u4e4e\u6240\u6709\u8ba1\u7b97\u5668\u578b\u53f7\u90fd\u5c06\u5176\u96c6\u6210\u5230\u5176\u8f6f\u4ef6\u4e2d\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u7531\u4e8e\u53ef\u4ee5\u4fdd\u5b58\u7ed3\u679c\uff0c\u60a8\u53ef\u4ee5<strong>\u4f7f\u7528\u9636\u4e58\u8fdb\u884c\u8fd0\u7b97<\/strong>\uff0c\u8fd9\u5bf9\u4e8e\u5728\u66f4\u77ed\u7684\u65f6\u95f4\u5185\u6267\u884c\u66f4\u591a\u8ba1\u7b97\u6709\u5f88\u5927\u5e2e\u52a9\u3002\u5982\u679c\u60a8\u60f3\u4e86\u89e3\u5982\u4f55\u66f4\u6709\u6548\u5730\u4f7f\u7528\u8ba1\u7b97\u5668\uff0c\u6211\u4eec\u8fd8\u5efa\u8bae\u60a8\u67e5\u770b\u6211\u4eec\u5173\u4e8e<a href=\"https:\/\/mathority.org\/cn\/\u5982\u4f55\u4f7f\u7528\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u4f7f\u7528\u79d1\u5b66\u8ba1\u7b97\u5668\u7684<\/a>\u6587\u7ae0\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"factorial-en-la-calculadora-casio-fx-991\"> <span id=\"Factorial_en_la_calculadora_Casio_FX-991\">Casio FX-991 \u8ba1\u7b97\u5668\u4e0a\u7684\u9636\u4e58<\/span><\/h2>\n<p>\u5728\u6587\u7ae0\u7684\u7ed3\u5c3e\uff0c\u6211\u4eec\u60f3\u8c08\u8c08<a href=\"https:\/\/mathority.org\/cn\" target=\"_blank\" rel=\"noreferrer noopener\">\u5361\u897f\u6b27 FX-911SPX 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