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.
[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.
Try $\displaystyle \int_{1}^{2}\frac{1}{x}dx$$\displaystyle \lim_{n\to {\infty}}\sum_{k=n}^{2n}\frac{1}{k}$
Try $\displaystyle \int_{0}^{1}\frac{x}{(1+x^{2})^{2}}dx$$\displaystyle \lim_{n\to {\infty}}\sum_{k=1}^{n}\frac{n^{2}k}{(n^{2}+k^{2}) ^{2}}$