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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.

2 Answers 2

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

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    Thank you. But I am not that clever really for posting this answer2012-12-07
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Not much different,$x^1+x^3+x^5\cdots=x(1+x^2+(x^2)^2+\cdots)$

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    Edited the formula, as it was not correct...2012-12-07