{"id":3110,"date":"2025-09-10T01:59:41","date_gmt":"2025-09-09T16:59:41","guid":{"rendered":"https:\/\/math-friend.com\/?p=3110"},"modified":"2025-09-10T02:17:17","modified_gmt":"2025-09-09T17:17:17","slug":"%e3%80%90%e5%8c%97%e6%b5%b7%e9%81%93%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%912012","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=3110","title":{"rendered":"\u3010\u5317\u6d77\u9053\u5927\u5b66\u5165\u8a66\u3011\u5148\u53d6\u52dd\u8ca0\u306e\u52dd\u7387\uff1a2\u672c\u5148\u53d6\u30683\u672c\u5148\u53d6(2012)"},"content":{"rendered":"\n<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n<p class=\"has-border -border02\">A\u3068B\u306e2\u30c1\u30fc\u30e0\u304c\u8a66\u5408\u3092\u884c\u3044, \u3069\u3061\u3089\u304b\u304c\u5148\u306b\\(k\\)\u52dd\u3059\u308b\u307e\u3067\u8a66\u5408\u3092\u7e70\u308a\u8fd4\u3059. \u5404\u8a66\u5408\u3067A\u304c\u52dd\u3064\u78ba\u7387\u3092\\(p\\), B\u304c\u52dd\u3064\u78ba\u7387\u3092\\(q\\)\u3068\u3057, \\(p+q=1\\)\u3068\u3059\u308b. A\u304cB\u3088\u308a\u5148\u306b\\(k\\)\u52dd\u3059\u308b\u78ba\u7387\u3092\\(P_k\\)\u3068\u304a\u304f.<br>(1) \\(P_2\\)\u3092\\(p\\)\u3068\\(q\\)\u3067\u8868\u305b.<br>(2) \\(P_2\\)\u3092\\(p\\)\u3068\\(q\\)\u3067\u8868\u305b.<br>(3) \\(\\displaystyle \\frac{1}{2}&lt;q&lt;1\\)\u306e\u3068\u304d, \\(P_3&lt;P_2\\)\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<br><span style=\"text-align:right;display:block;\">(2012 \u5317\u6d77\u9053\u5927\u5b66 \u6587\u7cfb [4])<\/span><\/p>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-crease\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>(1) \\(P_2\\)\u306fA\u304c\u5148\u306b\\(2\\)\u52dd\u3059\u308b\u78ba\u7387\u3067\u3042\u308a, A\u304c\\(2\\)\u52dd\u3057\u305f\u3068\u304d, \\(B\\)\u306f0\u52dd, \u307e\u305f\u306f1\u52dd\u3057\u3066\u3044\u308b. \u5404\u5834\u5408\u306b\u304a\u3044\u3066A\u304c\u5148\u306b\\(2\\)\u52dd\u3059\u308b\u78ba\u7387\u3092\u6c42\u3081\u308b.<br><br>\u2460 B\u304c\\(0\\)\u52dd\u3057\u3066\u3044\u308b\u5834\u5408<br>\u3053\u308c\u306f, A\u304c\\(2\\)\u9023\u52dd\u3059\u308b\u78ba\u7387\u306b\u306a\u308b\u306e\u3067, \u305d\u306e\u78ba\u7387\u306f\\(p^2\\)\u3067\u3042\u308b.<br><br>\u2461 B\u304c\\(1\\)\u52dd\u3057\u3066\u3044\u308b\u5834\u5408<br>\u3053\u308c\u306f\u6700\u521d\u306e\\(2\\)\u8a66\u5408\u3067A, B\u304c\u5171\u306b\\(1\\)\u52dd\u305a\u3064\u3057, \u6700\u5f8c\\(3\\)\u8a66\u5408\u76ee\u306bA\u304c\u52dd\u3064\u78ba\u7387\u3060\u304b\u3089,$$<br>{}_2\\mathrm{C}_1p^1q^1\\times p=2p^2q<br>$$\u3068\u306a\u308b.<br><br>\u2460, \u2461\u306f\u6392\u53cd\u306a\u306e\u3067,$$<br>P_2=p^2+2p^2q=p^2(1+2q)<br>$$\u3068\u306a\u308b.<\/p>\n\n\n\n<p>(2) \\(P_3\\)\u306fA\u304c\u5148\u306b\\(3\\)\u52dd\u3059\u308b\u78ba\u7387\u3067\u3042\u308a, A\u304c\\(3\\)\u52dd\u3057\u305f\u3068\u304d, \\(B\\)\u306e\u52dd\u5229\u6570\u306f0\u52dd, 1\u52dd, 2\u52dd\u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308b. \u5404\u5834\u5408\u306b\u304a\u3044\u3066A\u304c\u5148\u306b\\(3\\)\u52dd\u3059\u308b\u78ba\u7387\u3092\u6c42\u3081\u308b.<br><br>\u2460 B\u304c\\(0\\)\u52dd\u3057\u3066\u3044\u308b\u5834\u5408<br>\u3053\u308c\u306f, A\u304c\\(3\\)\u9023\u52dd\u3059\u308b\u78ba\u7387\u306b\u306a\u308b\u306e\u3067, \u305d\u306e\u78ba\u7387\u306f\\(p^3\\)\u3067\u3042\u308b.<br><br>\u2461 B\u304c\\(1\\)\u52dd\u3057\u3066\u3044\u308b\u5834\u5408<br>\u3053\u308c\u306f\u6700\u521d\u306e\\(3\\)\u8a66\u5408\u3067A\u304c\\(2\\)\u52dd, B\u304c\\(1\\)\u52dd\u3057, \u6700\u5f8c\\(4\\)\u8a66\u5408\u76ee\u306bA\u304c\u52dd\u3064\u78ba\u7387\u3060\u304b\u3089,$$<br>{}_3\\mathrm{C}_2p^2q^1\\times p=3p^3q<br>$$\u3068\u306a\u308b.<br><br>\u2462 B\u304c\\(2\\)\u52dd\u3057\u3066\u3044\u308b\u5834\u5408<br>\u3053\u308c\u306f\u6700\u521d\u306e\\(4\\)\u8a66\u5408\u3067A, B\u304c\u5171\u306b\\(2\\)\u52dd\u305a\u3064\u3057, \u6700\u5f8c\\(5\\)\u8a66\u5408\u76ee\u306bA\u304c\u52dd\u3064\u78ba\u7387\u3060\u304b\u3089,$$<br>{}_4\\mathrm{C}_2p^2q^2\\times p=6p^3q^2<br>$$\u3068\u306a\u308b.<br><br>\u2460, \u2461, \u2462\u306f\u6392\u53cd\u306a\u306e\u3067,$$<br>P_3=p^3+3p^3q+6p^3q^2=p^3(1+3q+6q^2)<br>$$\u3068\u306a\u308b.<\/p>\n\n\n\n<p>(3) \\(P_2-P_3>0\\)\u3092\u793a\u3059.$$<br>\\begin{align}<br>P_2-P_3&amp;=p^2(1+2q)-p^3(1+3q+6q^2)\\\\[1.5ex]<br>&amp;=p^2\\left\\{1+2q-p(1+3q+6q^2)\\right\\}\\\\[1.5ex]<br>&amp;=p^2\\left\\{1+2q-(1-q)(1+3q+6q^2)\\right\\}\\\\[1.5ex]<br>&amp;=p^2(1+2q-1-3q-6q^2+q+3q^2+6q^3)\\\\[1.5ex]<br>&amp;=p^2(6q^3-3q^2)\\\\[1.5ex]<br>&amp;=3p^2q^2(2q-1)<br>\\end{align}<br>$$\u3068\u306a\u308b\u304c, \\(\\displaystyle \\frac{1}{2}&lt;q&lt;1\\)\u3088\u308a, \\(2q-1>0\\), \\(p\\neq 0\\), \\(q\\neq 0\\)\u3067\u3042\u308b\u304b\u3089,$$<br>P_2-P_3=3p^2q^2(2q-1)>0<br>$$\u3067\u3042\u308b.<br><br>\u3088\u3063\u3066, \\(P_3&lt;P_2\\)\u304c\u308f\u304b\u308b.<\/p>\n<\/div><\/div>\n\n\n\n<p>youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/0pWIba6WY-U?si=mHdTVSpgNqFAGb8Y\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059. A\u3068B\u306e2\u30c1\u30fc\u30e0\u304c\u8a66\u5408\u3092\u884c\u3044, \u3069\u3061\u3089\u304b\u304c\u5148\u306b\\(k\\)\u52dd\u3059\u308b\u307e\u3067\u8a66\u5408\u3092\u7e70\u308a\u8fd4\u3059. \u5404\u8a66\u5408\u3067A\u304c\u52dd\u3064\u78ba\u7387\u3092\\(p\\), B\u304c\u52dd\u3064\u78ba\u7387\u3092\\(q\\)\u3068\u3057, \\(p+q=1\\)\u3068\u3059\u308b. A [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3115,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-3110","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tokimakuru"],"_links":{"self":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/3110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3110"}],"version-history":[{"count":7,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/3110\/revisions"}],"predecessor-version":[{"id":3119,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/3110\/revisions\/3119"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/media\/3115"}],"wp:attachment":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}