{"id":11895,"date":"2014-05-23T22:45:13","date_gmt":"2014-05-23T21:45:13","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11895"},"modified":"2022-01-13T11:11:24","modified_gmt":"2022-01-13T11:11:24","slug":"de-uma-sucessao-sabe-se-que-u_2011-102011-1","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11895","title":{"rendered":"De uma sucess\u00e3o sabe-se que ${u_{2011}} = {10^{2011}} + 1$"},"content":{"rendered":"<p><ul id='GTTabs_ul_11895' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11895' class='GTTabs_curr'><a  id=\"11895_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11895' ><a  id=\"11895_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_11895'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Seja $\\left( {{u_n}} \\right)$ uma sucess\u00e3o tal que: ${u_{2011}} = {10^{2011}} + 1$.<\/p>\n<ol>\n<li>A sucess\u00e3o\u00a0 \u00e9 um infinitamente grande positivo?<\/li>\n<li>Ser\u00e1 $\\left( {{u_n}} \\right)$\u00a0um infinitamente grande negativo?<\/li>\n<li>Ser\u00e1 que $\\left( {{u_n}} \\right)$\u00a0n\u00e3o \u00e9 um infinitamente grande?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11895' onClick='GTTabs_show(1,11895)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11895'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Seja $\\left( {{u_n}} \\right)$ uma sucess\u00e3o tal que: ${u_{2011}} = {10^{2011}} + 1$.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote><p>A sucess\u00e3o\u00a0 \u00e9 um infinitamente grande positivo?<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>Ser\u00e1 $\\left( {{u_n}} \\right)$\u00a0um infinitamente grande negativo?<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>Ser\u00e1 que $\\left( {{u_n}} \\right)$\u00a0n\u00e3o \u00e9 um infinitamente grande?<\/p><\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00ad<\/p>\n<p>A resposta a cada uma das quest\u00f5es anteriores \u00e9: <strong>N\u00e3o necessariamente<\/strong>.<\/p>\n<p>A t\u00edtulo de exemplo apresentam-se algumas possibilidades para $\\left( {{u_n}} \\right)$:<\/p>\n<ul>\n<li>Infinitamente grande positivo: \\[{u_n} = {10^n} + 1\\]<\/li>\n<li>Infinitamente grande negativo: \\[{u_n} = \\left( {2012 &#8211; n} \\right){10^n} + 1\\]<\/li>\n<li>Infinitamente grande (infinitamente grande em m\u00f3dulo): \\[{u_n} = {\\left( { &#8211; 1} \\right)^{n + 1}} \\times {10^n} + 1\\]<\/li>\n<li>Infinit\u00e9simo: \\[{u_n} = \\left( {{{10}^{2011}} + 1} \\right) \\times \\frac{{2011}}{n}\\]<\/li>\n<li>Convergente para $2014$: \\[{u_n} = \\left( {{{10}^{2011}} + 1 &#8211; 2014} \\right) \\times \\frac{{2011}}{n} + 2014\\]<\/li>\n<li>Oscilante: \\[{u_n} = \\left( {{{10}^{2011}} + 3} \\right) \\times \\frac{{2011}}{n} + 2 \\times {\\left( { &#8211; 1} \\right)^n}\\]<\/li>\n<\/ul>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11895' onClick='GTTabs_show(0,11895)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seja $\\left( {{u_n}} \\right)$ uma sucess\u00e3o tal que: ${u_{2011}} = {10^{2011}} + 1$. A sucess\u00e3o\u00a0 \u00e9 um infinitamente grande positivo? Ser\u00e1 $\\left( {{u_n}} \\right)$\u00a0um infinitamente grande negativo? Ser\u00e1 que $\\left( {{u_n}}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19171,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,372],"tags":[422,375,431],"series":[],"class_list":["post-11895","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-sucessoes-reais","tag-11-o-ano","tag-infinitamente-grande","tag-sucessoes-reais"],"views":3031,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat62.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11895","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11895"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11895\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19171"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11895"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11895"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11895"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}