(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Series Question (from a probability question)

EDIT: Found it, never mind.

Here is my question:

How do I find what [tex]\sum_{k=1}^{\infty}k(1/2)^k[/tex] is?

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Here is the original question and my work.

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A couple decides to continue to have children until a daughter is born. What is the expected number of children of this couple?

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So suppose P(having a daughter) = 1/2.

Define the random variable X = number of children until a daughter is born.

Then [itex]f_X(x) = (1-1/2)^{x-1}(1/2)[/itex]

So,

[tex]E(X) = \sum_{x = 1}^{\infty}x f_X(x) = \sum_{k=1}^{\infty}k(1/2)(1/2)^{k-1}[/tex]

or as I wrote it above.

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Now I believe everything I have done up this point is correct, however I can't remember how to do series. I have been looking at my calculus book, but I have yet to find what I need. Any hints would be greatly appreciated, thanks!

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EDIT: Found it online, seems to be a common geometric series, not sure why I couldn't find it in my book.

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# Homework Help: Series Question (from a probability question)

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