kleyzam,

For now I'll approach problem (2). I'm assuming you know the basics of expanding into partial fractions. If not, I suggest that you take a look in this material.

There must exist two numbers A and B such that

Now multiply both sides by :

Now you equate coefficients, and easily see that A = 2 and B = -2. So,

This is the very same process you use when evaluating intrincate polynomial integrals. If you've gone past Calculus 101 you might remember this, otherwise save this knowledge as it'll help you later.

So, for (a):

As for (b), are we supposed to calculate the series sum into infinity?