Question

How do you find the power series representation for the function `f(x)=1/(1-x)` ?

Answer 1

Remember that the sum of the geometric series can be found by
`a/{1-r}=sum_{n=0}^infty ar^n`.

By setting `a=1` and `r=x`,
`1/{1-x}=sum_{n=0}^infty x^n`.