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 which on first glance appeared to diverge but it actually converged when you used the fact below
If you can write as then we know
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