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Math Help - Real Analysis

  1. #1
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    Real Analysis

    is it true that 1-1/2+1/3-1/4=....=ln2??

    how i solve that question i have to use the harmonic series!?

    Thanks
    Nana
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  2. #2
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    Quote Originally Posted by NaNa View Post
    is it true that 1-1/2+1/3-1/4=....=ln2??

    how i solve that question i have to use the harmonic series!?

    Thanks
    Nana
    Substitute x = 1 into the Maclaurin series for ln(x + 1).
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  3. #3
    MHF Contributor chisigma's Avatar
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    Starting from the geometric series...

    \frac{1}{1+x} = 1 - x + x^{2} - x^{3} + ... , |x|<1 (1)

    ... and integrating term by term we obtain...

    \ln (1+x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + ... (2)

    Setting in (2) x=1 we have...

    \ln 2 = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + ... (3)

    Kind regards

    \chi \sigma
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  4. #4
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    So easy thanks a lot!!!
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