- #1

Eric Song

- 12

- 0

## Homework Statement

What is the power series for the function ln (x+1)? How do you find the sum of an infinite power series?

## Homework Equations

sigma from n=1 to infinity (-1)^n+1 (1/n2^n)

That is the power series, how is that equivalent to ln (x+1)?

How do you find the sum, or what does it converge to?

## The Attempt at a Solution

I know that the series converges via the ratio test: (-1)^n+2 (1/n2^n+1)/ (-1)^n+1 (1/n2^n) < 1.

So it converges, but how do I go from the power series to the function of ln(x+1)? I tried looking at known series, but still not sure. Also, how do I find the sum?