Recent content by bcucinel

Homework Statement Consider the power series Σanxn = 1+2x+3x2+x3+2x4+3x5+x6+… in which the coefficients an=1,2,3,1,2,3,1,... are periodic of period p=3. Find the radius of convergence. Homework Equations The Attempt at a Solution My attempt at a solution was to first state...

How exactly?

Thank you, I understand all of that perfectly... The issue I am having with the problem, however, is that I don't recall ever being taught in my calculus class exactly how to determine the Sn of a series like Σ1/(2n)²... If there is some technique that I could use please let me know.

1/4+1/16+1/36+... Σ1/n² - Σ1/(2n-1)² then equals Σ1/(2n)² from n=1 to infinity

Σ1/(2n-1)²: 1+1/9+1/25+1/49+1/81+... Σ1/n²: 1+1/4+1/9+1/16+1/25+...

When writing out the first few terms of Σ1/(2n-1)², I noticed that this represents the terms when n is some odd number from the first summation, ∑1/n², but I'm stuck as to the proof with setting that equal to 8.

My attempt which needs to be shown on paper... First I wrote out the first few terms of ∑(n=1) to (n=∞) of 1/n². So 1+1/4+1/9+1/16+...+1/n² = π²/6. I then just tried to simply substituted (2n-1) into the previous summation in place of just n to somehow show that ∑(n=1) to (n=∞) of...

Homework Statement It can be shown that ∑(n=1) to (n=∞) of 1/n² = π²/6 use this fact to show that ∑(n=1) to (n=∞) of 1/(2n-1)² = π²/8 Homework Equations The Attempt at a Solution