Find the Maclaurin series for f(x)=arctan(x)f(x) = \arctan(x)f(x)=arctan(x).
∑n=0∞(−1)nx2n+12n+1\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{2n+1}∑n=0∞(−1)n2n+1x2n+1
∑n=0∞x2n+12n+1\sum_{n=0}^{\infty} \frac{x^{2n+1}}{2n+1}∑n=0∞2n+1x2n+1
∑n=0∞(−1)nx2n2n\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n}}{2n}∑n=0∞(−1)n2nx2n
∑n=0∞(−1)nxnn!\sum_{n=0}^{\infty} (-1)^n \frac{x^n}{n!}∑n=0∞(−1)nn!xn