# Let X be a geometric random variable with parameter p compute E[X^3]

Let X be a geometric random variable with parameter $p$ compute $E[X^3]$.

How would I approach this and how would I simplify the series? Can I use a moment generating function?
I am able to write out a formula for expectation, I believe it is the sum from 1 to n of $k^3p(1-p)^{k-1}$, I apologize for the terrible notation but I am not sure how to proceed from here.

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Thank you! that was very helpful! –  Olivia Irving Dec 14 '12 at 2:04

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