Question

I am working on the taylor series portion of the course and had a question:

Answer 1

Is the taylor series representation of ln (x+1) = \[\sum_{0}^{\infty}((-1)^{n+1}X ^{n})/n\]

I worked this out on my own and wanted to know if this is correct. Thanks!

Answer 2

Correction I guess you have to start the series at 1 because of 0 being undefined.

Answer 3

Any ideas?

Answer 4

two ways i can think to approach this. one is to calculate the nth derivative of ln[1+x], and find \[(-1)^{n+1}/(1+x)^n\]
this value at x=0 is simply -(-1)^n or (-1)^(n+1) then proceed with taylor's formula.

else use the geometric series representation of closed form (assumes abs[x]<1)\[\frac{1}{1+x}=\sum_{n=0}^{\infty}(-x)^n\]
then integrate both sides with respect to x

Answer 5

Solved: Thanks gamesguru. I also just found out that Wikipedia has the Taylor series listed and my answer was right.