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Math Help - Challenging calculus problem

  1. #1
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    Challenging calculus problem

    the series (n=1 to infinity) (-1)^(n+1)/n and (n=1 to infinity) 1/n*2^(n) both converge to ln 2.

    1) How do we know?
    2) Which converges "faster" (i.e. gives a more efficient way to get a numerical approx.) To justify this, compute how many terms of each series must be added uup to approximate ln 2 with max. error 10^(-6)

    I don't know what to do at all here. Please help!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    partial answer anyway

    See attachment
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  3. #3
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    This is extremely helpful. Thank you very much!!
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