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....

2. 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 $\displaystyle f(x):=\frac{2x}{x+3}=\sum^\infty_{n=1}c_nx^n$ and differentiate on one hand the rational function and on the other hand the power series, and then compare each when taking $\displaystyle x=0$ ...

Tonio