Infinite Series: Find Function

[MrBailey]

Hello all!
I have the following infinite series:

\frac{10}{x}+\frac{10}{x^2}+\frac{10}{x^3}+\ldots

How would I find a function, f(x), of this series?

I know the series converges for \vert x \vert > 1

I think the function is: f(x) = \frac{10}{x-1}

but I'm not sure how to get it.

Thanks,
Bailey

 

[math-chick_41]

why the x-1 in the denominator?
maybe this


f_{n}(x) = \frac{10}{x^n}

because

\sum\frac{10}{x^n}

will be what you started with, but I may be worng and/or missing something though.

 

[Physics Monkey]

Hint: factor out a 10/x and see if the remaining series looks familiar to you.

 

[MrBailey]

Ugggh! I'm so blind sometimes...must be all the turkey I ate yesterday. I see the geometric series.

Thanks, PM.

Bailey