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Alternating Series convergence?
Is the series {(-1)^n sqrt(n) / (1+2sqrt(n))} n=1 to inf convergent? I don't know how to show the n+1 term is smaller (or larger) than the n term.
2 Answers
- ted sLv 71 decade agoFavorite Answer
does not meet the conditions of the AST...nth term does not tend to 0...{1/2}
- 1 decade ago
Lets take the alternating series part and summation part out for inspection
lim as n-> inf, sqrt(n) / (1+2sqrt(n))} = sqrt(n) / 2sqrt(n) = 1/2
=> Series is alternating between 1/2 and -1/2. It does not converge.