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Math Help - series

  1. #1
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    series

    lim(n tending to infinity) (1/(n+1)+1/(n+2)+.....+1/6n)=

    the sum of the above series is

    i have done by graph and answer is coming out to be ln6

    how should i solve theorotically
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: series

    \displaystyle\lim_{n \to{+}\infty}{\left(\dfrac{1}{n+1}+\dfrac{1}{n+2}+  \ldots+\dfrac{1}{6n}\right)}=

    \displaystyle\lim_{n \to{+}\infty}{\dfrac{1}{n}}\sum_{k=1}^{5n}\dfrac{1  }{1+k/n}=\int_0^5\dfrac{dx}{1+x}=\log 6
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