The Maclaurin series for ln(1+x) is
ln(1+x)=n=1∑∞n(−1)n+1xn(−1<x≤1).
Define f(x)=1+x1.
(a) Derive a power series representation for f(x) centered at x=0, clearly indicating the general term and the interval of convergence.
(b) Use your series to evaluate the infinite series n=1∑∞2n(−1)n+1n.