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Math Help - Maybe Reimann sums...

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Maybe Reimann sums...

    I need to compute the followings sums:

    1. lim(n-->inf)Sigma(k=n --> 2n) 1/k

    2. lim(n-->inf)Sigma(k=1 --> n) {(n^2 * k)/(n^2+k^2)^2}


    Thank you for your assistance.
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  2. #2
    Eater of Worlds
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    [quote=Also sprach Zarathustra;516517]I need to compute the followings sums:

    Yes, these do look like Riemann sums. Just look at them close and they kind of resemble something.


    \lim_{n\to {\infty}}\sum_{k=n}^{2n}\frac{1}{k}
    Try \int_{1}^{2}\frac{1}{x}dx


    \lim_{n\to {\infty}}\sum_{k=1}^{n}\frac{n^{2}k}{(n^{2}+k^{2})  ^{2}}
    Try \int_{0}^{1}\frac{x}{(1+x^{2})^{2}}dx
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    You have a very funny avatar, thats thing name?
    ...and I will try it right now, thank you!
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