{"id":11896,"date":"2014-05-24T00:18:40","date_gmt":"2014-05-23T23:18:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11896"},"modified":"2022-01-13T11:16:50","modified_gmt":"2022-01-13T11:16:50","slug":"prove-que-a-sucessao-e-um-infinitamente-pequeno","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11896","title":{"rendered":"Prove que a sucess\u00e3o \u00e9 um infinitamente pequeno"},"content":{"rendered":"<p><ul id='GTTabs_ul_11896' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11896' class='GTTabs_curr'><a  id=\"11896_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11896' ><a  id=\"11896_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_11896'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Prove que a sucess\u00e3o de termo geral ${v_n} = \\frac{5}{{n + 3}}$ \u00e9 um infinitamente pequeno.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11896' onClick='GTTabs_show(1,11896)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11896'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Prove que a sucess\u00e3o de termo geral ${v_n} = \\frac{5}{{n + 3}}$ \u00e9 um infinitamente pequeno.<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Seja $\\delta\u00a0 \\in {\\mathbb{R}^ + }$.<\/p>\n<p>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{\\left| {{v_n}} \\right| &lt; \\delta }&amp; \\Leftrightarrow &amp;{\\left| {\\frac{5}{{n + 3}}} \\right| &lt; \\delta } \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\frac{5}{{n + 3}} &lt; \\delta } \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{n\\delta\u00a0 + 3\\delta\u00a0 &gt; 5} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{n &gt; \\frac{{5 &#8211; 3\\delta }}{\\delta }}<br \/>\n\\end{array}\\]<\/p>\n<p>Conclui-se que $\\forall \\delta\u00a0 \\in {\\mathbb{R}^ + },\\,\\,\\exists p \\in \\mathbb{N}:\\,\\,n &gt; p \\Rightarrow \\left| {{v_n}} \\right| &lt; \\delta $.<\/p>\n<p>Logo, a sucess\u00e3o $\\left( {{v_n}} \\right)$ \u00e9 um infinitamente pequeno.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11896' onClick='GTTabs_show(0,11896)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Prove que a sucess\u00e3o de termo geral ${v_n} = \\frac{5}{{n + 3}}$ \u00e9 um infinitamente pequeno. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,372],"tags":[422,376,431],"series":[],"class_list":["post-11896","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-sucessoes-reais","tag-11-o-ano","tag-infinitesimo","tag-sucessoes-reais"],"views":7408,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11896","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=11896"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11896\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11896"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11896"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11896"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}