How do you find the power series representation for the function $f(x)=ln(5-x)$ ?

Question

4240 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-10-02T00:21:53

$f(x)=-sum_{n=1}^infty(x-4)^n/n$

Let us look at some details.

Since

$ln(1-x)=-sum_{n=1}^inftyx^n/n$ ,

by replacing $x$ by $(x-4)$ ,

$ln(5-x)=ln[1-(x-4)]=-sum_{n=1}^infty(x-4)^n/n$ .

.

How do you find the power series representation for the function f(x)=ln(5-x)f(x)=ln(5-x) ?