1. 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}

2. [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 $\int_{0}^{1}\frac{x}{(1+x^{2})^{2}}dx$

3. You have a very funny avatar, thats thing name?
...and I will try it right now, thank you!