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

Question

I would appreciate some directions regarding the follow problem,

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

Answer 1

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 $|x|\gt\frac12$.