Express f(x)=23−xf(x) = \frac{2}{3-x}f(x)=3−x2 as a power series centered at x=0x = 0x=0:
∑n=0∞2xn3n+1\sum_{n=0}^{\infty} \frac{2x^n}{3^{n+1}}∑n=0∞3n+12xn
∑n=0∞2xn3n\sum_{n=0}^{\infty} \frac{2x^n}{3^n}∑n=0∞3n2xn
∑n=0∞(−1)n2xn3n+1\sum_{n=0}^{\infty} \frac{(-1)^n 2x^n}{3^{n+1}}∑n=0∞3n+1(−1)n2xn
∑n=0∞xn3n\sum_{n=0}^{\infty} \frac{x^n}{3^n}∑n=0∞3nxn