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Math Help - log, riemann sums

  1. #1
    Senior Member slevvio's Avatar
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    log, riemann sums

    By considering a Riemann sum of a suitable function, show that

    ln2=\lim_{x\rightarrow\infty}(\sum_{r=1}^{n}\frac{  1}{n+r})

    This is perplexing me and any help would be appreciated, thanks.
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  2. #2
    Senior Member slevvio's Avatar
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    I actually just worked it out - here is my solution in case anyone is interested.

    \int_0^1f(x)dx = \lim_{n\rightarrow \infty}\frac{1}{n}f(\frac{r}{n})

    So \frac{1}{n}f(\frac{r}{n})=\frac{1}{n+r}

    f(\frac{r}{n})=\frac{n}{n+r}=\frac{1}{1+\frac{r}{n  }}

    So f(x)=\frac{1}{1+x}

    So R.H.S. = \int_0^1f(x)dx=\int_0^1\frac{1}{1+x}dx=ln2 = L.H.S.
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  3. #3
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    thanks

    yes thank you very much
    i understand
    btw how did u write the mathmatical symbols?
    did u copy from the microsoft word???
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  4. #4
    Super Member
    earboth's Avatar
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    Quote Originally Posted by xixihaha View Post
    ...
    btw how did u write the mathmatical symbols?
    did u copy from the microsoft word???
    Hi,

    have a look here: http://www.mathhelpforum.com/math-he...-tutorial.html
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