How do I evaluate infinite sums?

Question

I want to learn to add up all the terms so I can see whether it converges or diverges then solve for an exact number.

Answer 1

To check for convergence of a series, read the following tutorial:
http://www.math.unh.edu/~jjp/radius/radius.html

For a list of common infinite series, see:
http://math.bd.psu.edu/faculty/rutter/InfiniteSeries/CommonInfiniteSeries.html

Answer 2

You may be putting the cart before the horse. Usually you test for convergance or divergence, and then if there is convergence, find the sum.

Answer 3

It is frequently impossible to solve for the exact number, or in the very least, an incredibly difficult task (Geometric series excluded). It took Euler, one of the greatest mathematicians ever to live on this planet, several years to figure the exact sum of the series (1/n)^2 and, to my knowledge, no one knows the the exact value of (1/n)^3

Answer 4

use a computer program to add all the terms and check at each step if it converges or diverges