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Math Help - Integration by parts, limits

  1. #1
    Senior Member
    Joined
    Feb 2008
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    297

    Integration by parts, limits

    1) Show that \int_0^1 \ln (1+x) dx= -1 +\log 4

    2) Deduce that:

    \left(\left(1+\frac{1}{n}\right)\left(1+\frac{2}{n  }\right)...\left(1+\frac{n}{n}\right)\right)^{\fra  c{1}{n}} \rightarrow \frac{4}{e}\ as\ n \rightarrow \infty<br /> <br />
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  2. #2
    Senior Member
    Joined
    Feb 2010
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    To get 2, take logarithms and note that the LHS is a Riemann sum for the integral in 1.
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