Find the first three non-zero terms and the general term for the power series representation of f(x) = 1/(x^2 + 3).

Question

I came up with 1/3 - x^2/9 + x^4/27, but I don't know the general term.

Answer 1

something is wrong. Did you type it correctly? I cannot visualize how you get x in the numerator of any term, if f(x)= 1/(x^2+3)

Answer 2

of course f(x) can be expanded in a power series. A little playng around should convince you that

f(x) = sum(n=0..∞) (-1/3)^(n+1) x^(2n)

Answer 3

thanks steve.