# Two Power Series questions that need to be solved ly

1. Feb 5, 2010

### reichiru

Two Power Series questions that need to be solved urgently

1. The problem statement, all variables and given/known data
Question 1: The function f(x) = 2x (ln(1+x)) is represented as a power series. Find coefficients c2 through c6 of the power series.
Question 2: Write a partial sum for the power series which represents the function f(x) = 1/(1+(3^2)(x^2)) consisting of the first five non-zero terms. Also find the radius of convergence.

2. Relevant equations

3. The attempt at a solution
Question 1: Okay so the power series I came up with is (2(-1)n)/n x (xn), using the fact that ln(1+x) = 1/1+x = 1/1-(-x) and finding the partial sum 1-x+x^2-x^3... etc. So the coefficients I got were 1, 2/3, 1/2, 2/5, and 1/3. Unfortunately, the online thing says it's wrong, and I have no idea why...

Question 2: This one completely stumped me, the best I could come up with is to somehow take out the 3^2 so that you're left with 1+x^2 in the denominator, which is much easier to calculate a partial sum out of.

EDIT: Question 2 solved... just Question 1 now...
EDIT2: Never mind now, solved Question 1 as well.

Last edited: Feb 5, 2010