# Math Help - Challenging calculus problem

1. ## Challenging calculus problem

the series (n=1 to infinity) (-1)^(n+1)/n and (n=1 to infinity) 1/n*2^(n) both converge to ln 2.

1) How do we know?
2) Which converges "faster" (i.e. gives a more efficient way to get a numerical approx.) To justify this, compute how many terms of each series must be added uup to approximate ln 2 with max. error 10^(-6)