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

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Answer 1 · 2014-09-14T07:34:31

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 $r=x$ ,
$1/{1-x}=sum_{n=0}^infty x^n$ .

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