I have 2 general questions:

#1: How do I find the sum of a harmonic series? My book uses the example of the sum of 1/n from n=1 to infinity.

#2: So far, for all of the problems I've worked in which I'm asked to find if a given series converges/diverges and to find it's sum, the series has either been geometric or telescoping (sometimes after a bit of rearranging).

What's the general method for finding the sum if the series isn't geometric, telescoping, or harmonic? I think there is another kind called factorial, but I haven't learned that one yet.

Also, I'm aware of what the definition states; but if I could see an example problem worked in which the series cannot be transformed into any of the above, that would be wonderful. Thanks!