Find the Maclaurin series for f(x)=11+xf(x) = \frac{1}{1+x}f(x)=1+x1 and identify which statement is false.
The series is ∑n=0∞(−1)nxn=1−x+x2−x3+⋯\sum_{n=0}^{\infty} (-1)^n x^n = 1 - x + x^2 - x^3 + \cdots∑n=0∞(−1)nxn=1−x+x2−x3+⋯
The radius of convergence is R=1R = 1R=1
The series converges at x=−1x = -1x=−1
The coefficient of xnx^nxn is (−1)n(-1)^n(−1)n