Simplifying a Sum of Squared Terms: A Geometric Series Approach

[Nusc]

Homework Statement

How can I simplify sum from j=0 to infinite of x^(2j) ?

Homework Equations

The Attempt at a Solution

THis is close to the geometric series but I'd have to square each individual term

 

[sutupidmath]

well this looks like a gjeometric series, it will diverge for IxI>1, and it will converge for 0<IxI<1

what else are u looking for?

 

[sutupidmath]

Look at its partial sums, take the limit and you will get the result, i mean where it converges to for 0<IxI<1

 

[sutupidmath]

Ignore what i just said, in my posts #2,3
EDIT: Well don't ignore them, they seem to be right. Can you go from there?

 

[jambaugh]

You might also observe that $x^{2j} = (x^2)^j$ so start with the problem $\sum_{j=0}^\infty a^j$
and later set $a = x^2$

while you're at it recall how to factor differences of higher powers, e.g. $a^5 - 1 =$? There's a key formula you'll need.