Given ∑n=0∞xn=11−x\sum_{n=0}^{\infty} x^n = \frac{1}{1-x}∑n=0∞xn=1−x1 for ∣x∣<1|x|<1∣x∣<1, find the power series representation of f(x)=11−x2f(x) = \frac{1}{1-x^2}f(x)=1−x21.
∑n=0∞x2n\sum_{n=0}^{\infty} x^{2n}∑n=0∞x2n
∑n=0∞xn+2\sum_{n=0}^{\infty} x^{n+2}∑n=0∞xn+2
∑n=0∞2xn\sum_{n=0}^{\infty} 2x^n∑n=0∞2xn
∑n=0∞xn2\sum_{n=0}^{\infty} x^{n^2}∑n=0∞xn2