# 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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Xander Henderson, José Carlos Santos, Math Lover, Leucippus, Lee David Chung Lin
If this question can be reworded to fit the rules in the help center, please edit the question.

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

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 $$|x|\gt\frac12$$.