Find a power series for the function centered at c=0 and determine the interval of convergance. f(x)=4/(4+x^2)

f(x) = 4/(4+x^2) find power series and determine interval of convergence. need some help

Start with the geometric series 1/(1 - t) = Σ(n = 0 to ∞) t^n, convergent for |t| < 1.

Let t = -x^2/4:
1/(1 - (-x^2/4)) = Σ(n = 0 to ∞) (-x^2/4)^n, convergent for |-x^2/4| = |x^2|/4 < 1.
==> 4/(4 + x^2) = Σ(n = 0 to ∞) (-1/4)^n x^(2n), convergent for |x| < 2.

I hope this helps!