{"id":45451,"date":"2015-09-11T13:16:01","date_gmt":"2015-09-11T16:16:01","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=45451"},"modified":"2023-03-29T03:13:42","modified_gmt":"2023-03-29T06:13:42","slug":"problema-uma-potente-expressao","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-uma-potente-expressao\/","title":{"rendered":".Problema: Uma Potente Express\u00e3o"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\"  style=\"line-height:50px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 8\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nQual a soma dos algarismos do resultado da express\u00e3o [tex] \\, \\boxed{\\dfrac{2^{2015}+2^{2013}}{2^{2014}+2^{2012}} \\times 2014} [\/tex]?<\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p><\/p>\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Solu\u00e7\u00e3o <\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nObserve que <\/p>\n<p style=\"margin:10px\"><span style=\"font-size: 14px;\">[tex]\\qquad \\dfrac{2^{2015}+2^{2013}}{2^{2014}+2^{2012}} \\times 2014 = \\dfrac{2^{2013}(2^2+1)}{ 2^{2012}(2^2+1)} \\times 2014 = 2 \\times 2014 = 4028[\/tex]<\/span>.<\/p>\n<p>Assim, a soma dos algarismos de [tex]\\,\\dfrac{2^{2015}+2^{2013}}{2^{2014}+2^{2012}} \\times 2014\\, [\/tex] \u00e9:<br \/>\n[tex]\\qquad 4+0+2+8=\\fcolorbox{black}{#eee0e5}{$14$}\\,.[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" >Solu\u00e7\u00e3o elaborada pelo COM <strong> MIRIM APRENDIZ<\/strong>, com contribui\u00e7\u00f5es dos Moderadores do Blog.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g3\">\nParticipou da discuss\u00e3o o Clube <span style=\" color: #686461;\"><strong> MIRIM APRENDIZ<\/strong><\/span>.\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 8\u00ba ano do E. F.) Qual a soma dos algarismos do resultado da express\u00e3o [tex] \\, \\boxed{\\dfrac{2^{2015}+2^{2013}}{2^{2014}+2^{2012}} \\times 2014} [\/tex]? Solu\u00e7\u00e3o Observe que [tex]\\qquad \\dfrac{2^{2015}+2^{2013}}{2^{2014}+2^{2012}} \\times 2014 = \\dfrac{2^{2013}(2^2+1)}{ 2^{2012}(2^2+1)} \\times 2014 = 2 \\times 2014 = 4028[\/tex]. Assim, a soma dos algarismos de [tex]\\,\\dfrac{2^{2015}+2^{2013}}{2^{2014}+2^{2012}} \\times 2014\\, [\/tex] \u00e9: [tex]\\qquad &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-uma-potente-expressao\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-45451","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/45451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/164"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=45451"}],"version-history":[{"count":32,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/45451\/revisions"}],"predecessor-version":[{"id":185702,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/45451\/revisions\/185702"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=45451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}