What is the Maclaurin series for f(x)=11+x2f(x) = \frac{1}{1+x^2}f(x)=1+x21 for ∣x∣<1|x| < 1∣x∣<1?
∑n=0∞(−1)nx2n\sum_{n=0}^{\infty} (-1)^n x^{2n}∑n=0∞(−1)nx2n
∑n=0∞x2n\sum_{n=0}^{\infty} x^{2n}∑n=0∞x2n
∑n=0∞(−1)nxn\sum_{n=0}^{\infty} (-1)^n x^n∑n=0∞(−1)nxn
∑n=1∞(−1)nx2nn\sum_{n=1}^{\infty} \frac{(-1)^n x^{2n}}{n}∑n=1∞n(−1)nx2n