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Math Help - Harmonic series

  1. #1
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    Question Harmonic series

    How can I find N s.t.:
    1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{N}>10

    Thanks
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  2. #2
    Eater of Worlds
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    The harmonic series diverges very slowly.

    By the time you get to a sum of 10, you will have N=12,367
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by tunaaa View Post
    How can I find N s.t.:
    1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{N}>10
    Start by showing that 1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{N} \geqslant \ln(N+1).
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  4. #4
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    Thanks very much
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