{"id":228725,"date":"2026-05-12T15:00:06","date_gmt":"2026-05-12T18:00:06","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=228725"},"modified":"2026-05-12T15:00:32","modified_gmt":"2026-05-12T18:00:32","slug":"problemao-ali-babao-ataca-novamente-2-segunda-temporada","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problemao-ali-babao-ataca-novamente-2-segunda-temporada\/","title":{"rendered":".Problem\u00e3o: Ali Bab\u00e3o Ataca Novamente 2 &#8211; Segunda Temporada"},"content":{"rendered":"<div class=\"g1n\" style=\"line-height: 25px; padding-bottom: 15px;\">\n<p class=\"tit\" style=\"line-height: 25px; margin: 10px;\">Problema<br \/>\n<span style=\"font-size: 12px; color: #800000;\"> (Indicado a partir do 2\u00ba ano do E. M.)<\/span><\/p>\n<hr style=\"height: 1px; width: 100%; background-color: #800000; margin-top: 10px; margin-bottom: 20px; border: 0 none;\" \/>\nCalcule o valor de [tex]x[\/tex] de modo que:<\/p>\n<p><center>[tex]\\dfrac{(2x)!}{2^x \\cdot x! \\cdot 1\\cdot 3 \\cdot 5 \\cdot \\dots \\cdot (2x+1)}= \\dfrac {1}{9}.[\/tex]<br \/>\n<\/center><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"g1n\" style=\"line-height: 28px;\">\n<p class=\"tit\" style=\"line-height: 28px; margin: 10px;\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height: 1px; width: 100%; background-color: #800000; margin-top: 1px; margin-bottom: 20px; border: 0 none;\" \/>\nRepare que [tex]2 \\cdot 4 \\cdot 6 \\cdot \\dots \\cdot 2x = 2 \\cdot 1 \\cdot 2 \\cdot 2 \\cdot 2 \\cdot 3 \\cdot  \\dots \\cdot 2\\cdot x = 2^{x} \\cdot x![\/tex].<\/p>\n<p>Ent\u00e3o, a equa\u00e7\u00e3o<br \/>\n<center>[tex]\\dfrac{(2x)!}{2^x \\cdot x! \\cdot 1\\cdot 3 \\cdot 5 \\cdot \\dots \\cdot (2x+1)}= \\dfrac {1}{9}[\/tex]<br \/>\n<\/center><br \/>\npode ser escrita da seguinte forma:<\/p>\n<p><center>[tex]\\dfrac{(2x)!}{(2 \\cdot 4 \\cdot 6 \\cdot \\dots \\cdot 2x) \\cdot 1\\cdot 3 \\cdot 5 \\cdot \\dots \\cdot (2x+1)}= \\dfrac{(2x)!}{(2x+1)!}=\\dfrac {1}{9}[\/tex].<\/center><\/p>\n<p>Assim,<br \/>\n<center>[tex]\\dfrac{(2x)!}{(2x+1)!}=\\dfrac{\\cancel{(2x)!}}{\\cancel{(2x)!}(2x+1)}=\\dfrac{1}{9}.[\/tex] <\/center><\/p>\n<p>Segue que [tex] 2x+1=9[\/tex], ou seja, [tex]x=4[\/tex].<\/center><\/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 pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 2\u00ba ano do E. M.) Calcule o valor de [tex]x[\/tex] de modo que: [tex]\\dfrac{(2x)!}{2^x \\cdot x! \\cdot 1\\cdot 3 \\cdot 5 \\cdot \\dots \\cdot (2x+1)}= \\dfrac {1}{9}.[\/tex] &nbsp; Solu\u00e7\u00e3o Repare que [tex]2 \\cdot 4 \\cdot 6 \\cdot \\dots \\cdot 2x = 2 \\cdot 1 \\cdot 2 \\cdot 2 \\cdot 2 &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problemao-ali-babao-ataca-novamente-2-segunda-temporada\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":668,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-228725","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/228725","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\/668"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=228725"}],"version-history":[{"count":11,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/228725\/revisions"}],"predecessor-version":[{"id":229499,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/228725\/revisions\/229499"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=228725"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}