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Math Help - Absolute convergence

  1. #1
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    Absolute convergence

    Determine whether the series (-1)k-11/k+K^1/2 converges absolutely, converges conditionally, or diverges. (summation goes to infinity and starts at k=1)

    i don't think it converges absolutely, but im really not sure how to test for conditional convergence. thanks in advance
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  2. #2
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    Re: Absolute convergence

    Quote Originally Posted by chizmin10 View Post
    Determine whether the series (-1)k-11/k+K^1/2 converges absolutely, converges conditionally, or diverges. (summation goes to infinity and starts at k=1)

    i don't think it converges absolutely, but im really not sure how to test for conditional convergence. thanks in advance
    At the moment this is unreadable. Please use brackets where they're needed, or better yet, learn some LaTeX.

    Is this your summand? \displaystyle \begin{align*} \frac{(-1)^{k-1}}{k + k^{\frac{1}{2}}} \end{align*}
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    Re: Absolute convergence

    no thats not it. its ((-1)^k-1)(1/(k+sqrtk))
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    Re: Absolute convergence

    Quote Originally Posted by chizmin10 View Post
    no thats not it. its ((-1)^k-1)(1/(k+sqrtk))
    Do you understand that \sqrt{k}=k^{\frac{1}{2}}~?
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  5. #5
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    Re: Absolute convergence

    What does the alternating series test tell you?
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