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!

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!

eazye_the_best · Answer

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.

mww · Answer

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

cocoacat · Answer

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