Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How do I find the explicit formula for the following summation: $x^1 + x^3 + x^5 + ... $

I know $1 + x + x^2 + x^3 + ... = 1/(1-x)$, but this is quite a different series.

share|cite|improve this question

2 Answers 2

up vote 6 down vote accepted

$$x+x^3+x^5+....=x(1+x^2+x^4+....)=x(1+(x^2)^1+(x^2)^2+(x^2)^3+....)=\frac {x}{1-x^2}$$

share|cite|improve this answer
Thanks! why didnt I think of this?! – 0x56794e Dec 7 '12 at 11:19
So clever, Amr! :-) – 000 Dec 7 '12 at 11:29
Thank you. But I am not that clever really for posting this answer – Amr Dec 7 '12 at 11:30

Not much different,$$x^1+x^3+x^5\cdots=x(1+x^2+(x^2)^2+\cdots)$$

share|cite|improve this answer
Edited the formula, as it was not correct... – Jan Keersmaekers Dec 7 '12 at 11:06

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.