{"id":11891,"date":"2014-05-22T20:50:14","date_gmt":"2014-05-22T19:50:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11891"},"modified":"2022-01-13T10:55:11","modified_gmt":"2022-01-13T10:55:11","slug":"a-sucessao-e-monotona-e-limitada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11891","title":{"rendered":"A sucess\u00e3o \u00e9 mon\u00f3tona? E limitada?"},"content":{"rendered":"<p><ul id='GTTabs_ul_11891' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11891' class='GTTabs_curr'><a  id=\"11891_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11891' ><a  id=\"11891_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_11891'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A sucess\u00e3o de termo geral ${u_n} = n &#8211; {\\left( { &#8211; 1} \\right)^n}$ \u00e9 limitada? E mon\u00f3tona?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11891' onClick='GTTabs_show(1,11891)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11891'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A sucess\u00e3o de termo geral ${u_n} = n &#8211; {\\left( { &#8211; 1} \\right)^n}$ \u00e9 limitada? E mon\u00f3tona?<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Ora, ${u_n} = n &#8211; {\\left( { &#8211; 1} \\right)^n} = \\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{n + 1}&amp; \\Leftarrow &amp;{n\\,\\,{\\text{\u00edmpar}}} \\\\<br \/>\n{n &#8211; 1}&amp; \\Leftarrow &amp;{n\\,\\,{\\text{par}}}<br \/>\n\\end{array}} \\right.$.<\/p>\n<p>Como ${u_1} = 2$, ${u_2} = 1$ e ${u_3} = 4$, ent\u00e3o a sucess\u00e3o n\u00e3o \u00e9 mon\u00f3tona, pois ${u_1} &gt; {u_2} &lt; {u_3}$.<\/p>\n<p>\u00adSeja\u00a0$M \\in {\\mathbb{R}^ + }$.<\/p>\n<p>Como a condi\u00e7\u00e3o ${u_n} &gt; M$ \u00e9 poss\u00edvel para todo o $M \\in {\\mathbb{R}^ + }$, ent\u00e3o a sucess\u00e3o n\u00e3o \u00e9 limitada superiormente, pois existem termos da sucess\u00e3o que s\u00e3o superiores\u00a0a $M$.<\/p>\n<p>Portanto, $\\left( {{u_n}} \\right)$, ainda que limitada inferiormente, n\u00e3o \u00e9 uma sucess\u00e3o limitada.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11891' onClick='GTTabs_show(0,11891)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A sucess\u00e3o de termo geral ${u_n} = n &#8211; {\\left( { &#8211; 1} \\right)^n}$ \u00e9 limitada? E mon\u00f3tona? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,372],"tags":[422,294,373,431],"series":[],"class_list":["post-11891","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-sucessoes-reais","tag-11-o-ano","tag-monotonia","tag-sucessao-limitada","tag-sucessoes-reais"],"views":11200,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat65.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11891","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=11891"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11891\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19174"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11891"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}