Use o Teste da Razão para determinar se as seguintes séries são absolutamente convergentes, condicionalmente convergentes ou divergentes. (a) ∑+∞...
(a) ∑+∞ n=1 (-1)^(n+1)/(n^(2n))
(b) ∑+∞ n=1 (-2/3)^n/n
(c) ∑+∞ n=1 n^2/n!
(d) ∑+∞ n=1 (-1)^(n+1)/(n(n+2))
(e) ∑+∞ n=1 sin(πn)/n
💡 1 Resposta
Ed 
Vamos analisar cada série utilizando o Teste da Razão: (a) ∑+∞ n=1 (-1)^(n+1)/(n^(2n)) Para aplicar o Teste da Razão, vamos calcular o limite de |a(n+1)/a(n)| quando n tende ao infinito: lim n→∞ |((-1)^(n+2)/((n+1)^(2(n+1)))) / ((-1)^(n+1)/(n^(2n)))| Simplificando, temos: lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((n+1)^(2(n+1))) * (-1)^(n+1)| lim n→∞ |(-1)^(n+2) * n^(2n) / ((
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