{"id":375,"date":"2012-04-20T01:24:30","date_gmt":"2012-04-19T16:24:30","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=375"},"modified":"2021-09-24T17:44:23","modified_gmt":"2021-09-24T08:44:23","slug":"tok201202","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201202\/","title":{"rendered":"\u6771\u5de5\u59272012\uff1a\u7b2c2\u554f"},"content":{"rendered":"<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(\\log _ {10} 3 = 0.4771\\) \u3068\u3057\u3066, \\(\\textstyle\\sum\\limits _ {n=0}^{99} 3^n\\) \u306e\u6841\u6570\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057\u3066, \\(a\\) \u3092\u8d85\u3048\u306a\u3044\u6700\u5927\u306e\u6574\u6570\u3092 \\([a]\\) \u3067\u8868\u3059. \\(10000\\) \u4ee5\u4e0b\u306e\u6b63\u306e\u6574\u6570 \\(n\\) \u3067 \\(\\left[ \\sqrt{n} \\right]\\) \u304c \\(n\\) \u306e\u7d04\u6570\u3068\u306a\u308b\u3082\u306e\u306f\u4f55\u500b\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(I = \\textstyle\\sum\\limits _ {n=0}^{99} 3^n\\) \u3068\u304a\u304f.\r\n\\[\r\nI = \\dfrac{3^{100}-1}{3-1} =\\dfrac{3^{100} -1}{2}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066,\r\n\\[\\begin{align}\r\n3^{99} & \\lt I \\lt 3^{100} \\\\\r\n\\text{\u2234} \\quad \\log _ {10} 3^{99} & \\lt \\log _ {10} I \\lt \\log _ {10} 3^{100} \\\\\r\n\\end{align}\\]\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n\\log _ {10} 3^{99} & = 99 \\cdot 0.4771 = 47.2329 , \\\\\r\n\\log _ {10} 3^{100} & = 100 \\cdot 0.4771 = 47.71\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n\\log _ {10} I = 47. \\cdots\r\n\\]\r\n\u3088\u3063\u3066 \\(I\\) \u306e\u6841\u6570\u306f, \\(\\underline{48}\\) .<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\([ \\sqrt{n} ] = m\\) \uff08 \\(m\\) \u306f\u81ea\u7136\u6570\uff09\u3068\u306a\u308b\u306e\u306f\r\n\\[\r\nm^2 \\leqq n \\leqq (m+1)^2 -1 = m(m+2) \\quad ... [1]\r\n\\]\r\n\u3092 \\(n\\) \u304c\u307f\u305f\u3059\u3068\u304d\u3067\u3042\u308b.\r\n[1]\u306e\u7bc4\u56f2\u306b\u306f \\(m\\) \u306e\u500d\u6570\u304c \\(3\\) \u3064\uff08 \\(m^2 , m(m+1) , m(m+2)\\) \uff09\u542b\u307e\u308c, \\(10000 =100^2\\) \u3067\u3042\u308b\u3053\u3068\u304b\u3089, \u3082\u3068\u3081\u308b\u500b\u6570\u306f\r\n\\[\r\n99 \\cdot 3 +1 = \\underline{298 \\text{\u500b}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\\(\\log _ {10} 3 = 0.4771\\) \u3068\u3057\u3066, \\(\\textstyle\\sum\\limits _ {n=0}^{99} 3^n\\) \u306e\u6841\u6570\u3092\u6c42\u3081\u3088. (2)\u3000\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057\u3066, \\(a &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tok201202\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[61],"tags":[141,68],"class_list":["post-375","post","type-post","status-publish","format-standard","hentry","category-toko_2012","tag-toko","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=375"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/375\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}