{"id":68668,"date":"2016-11-21T01:11:24","date_gmt":"2016-11-21T03:11:24","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=68668"},"modified":"2023-04-05T00:08:54","modified_gmt":"2023-04-05T03:08:54","slug":"desafio-sera-que-sei-somar","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/desafio-sera-que-sei-somar\/","title":{"rendered":".Desafio: Ser\u00e1 que sei somar?"},"content":{"rendered":"

\n

\n

Problema
\n (Indicado a partir do 7\u00ba ano do E. F.)<\/span><\/p>\n

\nEncontre a soma
\n[tex]\\qquad \\qquad6 + 66 + 666 + \\ldots + \\overbrace{666\\ldots6}^{100\\,\\,d\u00edgitos}[\/tex]. <\/p>\n

\n

Justifique sua resposta.<\/p>\n

\n

<\/strong><\/div>\n

\n

\n

Solu\u00e7\u00e3o <\/p>\n

\n[tex]6 + 66 + 666 + \\ldots + \\overbrace{666\\ldots6}^{100\\,\\,d\u00edgitos}=[\/tex]<\/p>\n

[tex]= 6 \\cdot (1 + 11 + 111 + \\ldots + \\overbrace{111\\ldots1}^{100\\,\\,d\u00edgitos})[\/tex]<\/p>\n

[tex]= \\dfrac{6}{9} \\cdot (9 + 99 + 999 + \\ldots + \\overbrace{999\\ldots9}^{100\\,\\,d\u00edgitos})[\/tex]<\/p>\n

[tex]= \\dfrac{2}{3} \\cdot (10 – 1 + 100 – 1 + 1000 – 1 + \\ldots + 1\\overbrace{000\\ldots0}^{100\\,\\,d\u00edgitos} – 1)[\/tex]<\/p>\n

[tex]= \\dfrac{2}{3} \\cdot (10 + 100 + 1000 + \\ldots + 1\\overbrace{000\\ldots0}^{100\\,\\,d\u00edgitos} – 100)[\/tex]<\/p>\n

[tex]= \\dfrac{2}{3} \\cdot (\\overbrace{111\\ldots1}^{100\\,\\,d\u00edgitos}0 – 100)[\/tex]<\/p>\n

[tex]= \\dfrac{2}{3} \\cdot (\\overbrace{111\\ldots1}^{99\\,\\,d\u00edgitos}00 – 90)[\/tex]<\/p>\n

[tex]= 2 \\cdot (\\overbrace{37037\\ldots037}^{98\\,\\,d\u00edgitos}00 – 30)[\/tex]<\/p>\n

[tex]= \\overbrace{740740\\ldots740}^{99\\,\\,d\u00edgitos}0 – 60[\/tex]<\/p>\n

[tex]= \\overbrace{740740\\ldots740}^{96\\,\\,d\u00edgitos}7400 – 60[\/tex]<\/p>\n

[tex]= \\overbrace{740740\\ldots740}^{96\\,\\,d\u00edgitos}7340[\/tex]<\/p>\n

\n

Solu\u00e7\u00e3o elaborada pelos Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Problema (Indicado a partir do 7\u00ba ano do E. F.) Encontre a soma [tex]\\qquad \\qquad6 + 66 + 666 + \\ldots + \\overbrace{666\\ldots6}^{100\\,\\,d\u00edgitos}[\/tex]. Justifique sua resposta. Solu\u00e7\u00e3o [tex]6 + 66 + 666 + \\ldots + \\overbrace{666\\ldots6}^{100\\,\\,d\u00edgitos}=[\/tex] [tex]= 6 \\cdot (1 + 11 + 111 + \\ldots + \\overbrace{111\\ldots1}^{100\\,\\,d\u00edgitos})[\/tex] [tex]= \\dfrac{6}{9} \\cdot (9 + 99 + … <\/p>\n

Continue lendo<\/a><\/p>\n","protected":false},"author":179,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-68668","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/68668","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\/179"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=68668"}],"version-history":[{"count":12,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/68668\/revisions"}],"predecessor-version":[{"id":186292,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/68668\/revisions\/186292"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=68668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}