- #1

bonfire09

- 249

- 0

## Homework Statement

At what points ##x## in the interval ##(-1,1]## can one use the Lagrange Remainder Theorem to verify the expansion

##ln(1+x)=\sum_{k=1}^{\infty} (-1)^{k+1}{\frac{x^k}{k!}}##

## Homework Equations

## The Attempt at a Solution

Now I know that ##ln(1+x)=\sum_{k=1}^{\infty} (-1)^{k+1}{\frac{x^k}{k}}## when ##x\in(-1,1]##. If we let ##P_n## denote the nth Taylor polynomial for ##ln(1+x)## then ##f(x)-P_n(x)=\frac{(-1)^{n+1}}{(n+1)(1+c)^{n+1}}x^{n+1}## centered at ##0##.

The only difference between these two forms is the ##k!## which I'm not sure how to deal with. Also if you could provide me with some hint on how to go about this problem that be great thanks.

Last edited: