{"id":46,"date":"2004-11-17T19:34:01","date_gmt":"2004-11-17T19:34:01","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=46"},"modified":"2004-11-17T19:34:01","modified_gmt":"2004-11-17T19:34:01","slug":"nice-problem","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=46","title":{"rendered":"Nice Problem"},"content":{"rendered":"<p>Here&#8217;s a nice problem taken from <a href=\"http:\/\/www.tangentspace.net\/cz\/\" target=\"_blank\">ChapterZero<\/a> who, in turn, got it from <a href=\"http:\/\/www.amazon.co.uk\/exec\/obidos\/ASIN\/0070856133\/qid=1100853493\/ref=sr_8_xs_ap_i1_xgl\/202-9748268-2897441\" target=\"_blank\">Rudin&#8217;s Principles of Mathematical Analysis<\/a><\/p>\n<ul><i>Given the sequence <img src='\/maths\/latexrender\/pictures\/dcf1cc94915dcd2f1db2112b943f5358.gif' title='{s_n}' alt='{s_n}' align=absmiddle> defined as <img src='\/maths\/latexrender\/pictures\/d735dc7f56cde94ff53f0a4543dc0a9a.gif' title='s_1=\\sqrt{2},\\ s_{n+1}=\\sqrt{2+\\sqrt{s_n}}' alt='s_1=\\sqrt{2},\\ s_{n+1}=\\sqrt{2+\\sqrt{s_n}}' align=absmiddle>, show that <img src='\/maths\/latexrender\/pictures\/dcf1cc94915dcd2f1db2112b943f5358.gif' title='{s_n}' alt='{s_n}' align=absmiddle> converges, and that it is bounded above by 2<\/i>.<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Here&#8217;s a nice problem taken from ChapterZero who, in turn, got it from Rudin&#8217;s Principles of Mathematical Analysis Given the sequence defined as , show that converges, and that it is bounded above by 2.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-46","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/46","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=46"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/46\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=46"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=46"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=46"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}