Hey guys, I know this is a weird question but here it goes.. I few years ago I remember seeing an infinite series of the form $\displaystyle \sum_{i=1}^\infty g(i)$ which on first glance appeared to diverge but it actually converged when you used the fact below

If you can write $\displaystyle \sum_{i=1}^\infty g(i)$ as $\displaystyle \lim_{n\rightarrow\infty}\sum_{i=1}^n f\Big (\frac{i}{n}\Big )\frac{1}{n}$ then we know $\displaystyle \sum_{i=1}^\infty g(i)=\int_0^1 f(x)dx$

Essentially I am looking for an example which appears to diverge, but can be turned into a Riemann integral which can be calculated to prove convergence.

I am having a very hard time trying to remember/create such an example. Does anyone know of an example like this? If it's not clear what I'm talking about, the general version of the "fact" I mention can be found here as the corollary at the bottom [HTML]http://www.math.nus.edu.sg/~matngtb/Calculus/Riemannsum/Riemannsum.htm[/HTML]

Thanks for all help