When is it ok to interchange integration with summation to infinity?
If the partial sums of the summation converge uniformly.
In your case, a way to test for uniform convergence is the Weierstrass M test.
Thanks to all of you. I had a sum a while ago which to this day I cannot perform: 1/((n+1)(2n+1)(3n+1)), n=0,...,infinity. I tried using the trick of interchanging the summation with integration there and it didn't work. I'm wondering, is there another way of doing this sum?
My previous thread about this subject: http://www.mathhelpforum.com/math-he...ce-156957.html
Mathematica gives two different numerical answers.
My approach to complicated sums is to express them as integrals. Being a physicist, I find it easier to think in terms of integrals than sums. You can always transform a number into a definite integral. The question is to choose the simplest integral. This is where I sometimes need help from you guys