1. ## Power Series

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

If we have:
$\sum_{n=0}^{\infty}$ a_n*x^n = $\sum_{n=0}^{\infty}$ 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.)

2. Originally Posted by ajj86
This is number 4 of the set of real analysis questions:

If we have:
$\sum_{n=0}^{\infty}$ a_n*x^n = $\sum_{n=0}^{\infty}$ 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.)
If ture for all x then certain true for $x = 0$ and after substituting this all the terms dissappear except $a_0 = b_0$

$\sum_{n=1}^{\infty} a_n x^n = \sum_{n=1}^{\infty} b_n x^n$

Then, cancel and x and repeat.