Thread: Problem understanding power series and radius of convergence....please help

I must be really stupid because everyone says these are really easy but I just don't get it. Even the tutor at the math lab said he couldn't help because I didn't get it.

So, anyways....

The problem is "suppose that 2x/(3+x)= sum cn x^n from n=0 to inf
Find the first few coefficients and R

I found c0 by just replacing n with 0 which gets 0.
I found c1 on accident 2/3

I don't know how to find R or c2,c3,c4

I thought this was the same as sum ax^n with a being 2x/(3+x) but I must be wrong.

I swear this is the last time I am taking a math class online with no help from the professor....

Originally Posted by operaphantom2003

I must be really stupid because everyone says these are really easy but I just don't get it. Even the tutor at the math lab said he couldn't help because I didn't get it.

So, anyways....

The problem is "suppose that 2x/(3+x)= sum cn x^n from n=0 to inf
Find the first few coefficients and R

I found c0 by just replacing n with 0 which gets 0.
I found c1 on accident 2/3

I don't know how to find R or c2,c3,c4

I thought this was the same as sum ax^n with a being 2x/(3+x) but I must be wrong.

I swear this is the last time I am taking a math class online with no help from the professor....

Put and differentiate on one hand the rational function and on the other hand the power series, and then compare each when taking ...

Tonio