I will help with the first....but...for the second...physics ::shivers::.

a) So first we must find an expression for

We first note (I assume you know this) that

So now if we substitute in we get

And noting that and that since a variable is a variable let us just replace with x[/tex]. So

b) So since this series converges for all real values we can say it converges on any . So now let us consider

And since integrating a power series changes the endpoints of its interval of convergence we are done (because the set of real numbers does not have endpoints)

c) So you must just calculate where is given by the first integer that makes

Ok...lets do this

a) Just multiply by

b) Why dont you take a stab at this

Hint: Consider