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Math Help - Converge or diverge

  1. #1
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    Converge or diverge

    hi everyone,

    need help with this question

    Test the alternating series for convergence or divergence.

    \sum ^\infty_{n=1} \frac {(-1)^{n-1}}{n^ \frac{1}{2}}

    can anyone help offer some guide, i'm stuck.

    thank you & regards,really appreciate all your help.
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by anderson View Post
    hi everyone,

    need help with this question

    Test the alternating series for convergence or divergence.

    \sum ^\infty_{n=1} \frac {(-1)^{n-1}}{n^ \frac{1}{2}}

    can anyone help offer some guide, i'm stuck.

    thank you & regards,really appreciate all your help.
    The alternating series has a well-known test for testing its convergence/divergence.
    Do you know this test ?
    Can you apply it on this problem ?
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  3. #3
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    hi General

    i know the test but i doint know how to apply for this question. please help clarify,really hope someone can help me out.
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  4. #4
    Super Member General's Avatar
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    Quote Originally Posted by anderson View Post
    hi General

    i know the test but i doint know how to apply for this question. please help clarify,really hope someone can help me out.
    For the series \sum_{n=1}^{\infty} (-1)^{n-1} b_n , if:

    1- b_n > 0 \,\ \forall \,\ n \geq 1

    2- b_n \geq b_{n+1} for all n \geq 1 , i.e. b_n is decreasing.

    3- \lim_{n\to\infty} b_n = 0.

    Then the series converges.

    Now, for your problem b_n=\frac{1}{n^\frac{1}{2}}=\frac{1}{\sqrt{n}}.

    Can you apply the test on it?
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  5. #5
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    Hi General

    thank you so much for explaining,really appreciate
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