Question

Hey guys need some help with series!

Consider an infinite geometric series of positive terms that converges to S. What fractional part of S is the sum of the odd-numbered terms? Give answers in terms of r, the common ratio of the series.

So I know I will have to do (Sum of odd numbers)/(Normal sum formula, a/1-r) and that will cancel a and give me the answer in terms of r. I'm just confused as to how to find the sum of odd numbers.

Thanks!

Answer 1

First you would go with the odd numbers you can think of then go onto the internet and find a resource for all of the odd numbers there are. And there you go.

Answer 2

Hint: find sum of a+ar^2 + ar^4 + ar^6 +...+ar^(n-1) for some odd n.

Answer 3

Figured it out! a/1-r^2, thanks @mww