I do not understand how to go about the following proof, any suggestions?

Suppose f(x) = a0 + a1x + a2x2 + a3x3 + a4x4 + ... for x in an interval

(-R, R).

If f is even, prove that:

0 = a1 = a3 = a5 = a7 = ...

If f is odd, prove that:

0 = a0 = a2 = a4 = a6 = ...

Hint. The coefficients of a power series converging on an interval have to

be the Taylor coefficients of the function that the series converges to. Thus

it is not possible for different power series to converge to the same function

on an interval (-R, R).