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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

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  • ted s
    Lv 7
    1 decade ago
    Favorite 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.

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