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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- May 21st 2010, 04:44 AMAlso sprach ZarathustraMaybe 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. - May 21st 2010, 12:56 PMgalactus
[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.

Quote:

$\displaystyle \lim_{n\to {\infty}}\sum_{k=n}^{2n}\frac{1}{k}$

Quote:

$\displaystyle \lim_{n\to {\infty}}\sum_{k=1}^{n}\frac{n^{2}k}{(n^{2}+k^{2}) ^{2}}$

- May 21st 2010, 01:27 PMAlso sprach Zarathustra
You have a very funny avatar, thats thing name?

...and I will try it right now, thank you!