This is number 4 of the set of real analysis questions:

If we have:

$\displaystyle \sum_{n=0}^{\infty} $ a_n*x^n = $\displaystyle \sum_{n=0}^{\infty} $ b_n*x^n

for all x in an interval (-R,R), prove that a_n = b_n for all n = 0,1,2...

(Start by showing that a_0 = b_0.)