# What is the sum $\sum_{k=10}^{\infty}\left(\frac{1}{2x}\right)^k$ [closed]

I would appreciate some directions regarding the follow problem,

$$\sum_{k=10}^{\infty}\left(\frac{1}{2x}\right)^k=$$?

## closed as off-topic by Xander Henderson, José Carlos Santos, Math Lover, Leucippus, Lee David Chung LinApr 9 at 0:29

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• What have you tried? Where are you stuck? Are you familiar with geometric series? – avs Apr 8 at 21:56

## 1 Answer

This is an infinite geometric summation with $$a=\frac{1}{(2x)^{10}}=\frac1{1024x^{10}}$$ and common ratio $$r=\frac1{2x}$$ hence the summation is equal to $$S_{\infty}=\frac{a}{1-r}=\frac{\left(\frac1{1024x^{10}}\right)}{\left(1-\frac1{2x}\right)}=\frac1{512x^9(2x-1)}$$ Assuming that $$|x|\gt\frac12$$.