Determine wheter the sum from n=2 to infinity of ((-1)^(n+1))/(ln(n)) converges absolutely, converges conditionally, or diverges. Also assume you have a supercomputer that can add 10^15 terms per second (which is very fast for even a supercomputer). If you wanted to estimate the sum to within an error of .01, how long would this take? Give your answer in years. preferably in scientific notation. In what state will you find the Earth when your computer has completed this computation? When I first started trying this problem, I attempted using the Power series, as it's something we've been recently covering in class. Today we went over the derivatives and antiderivatives of functions such as this, and their relation to each other. The major place where I'm running into trouble is with the imaginary supercomputer thing. Also, I'm not sure if I'm starting in the right place? I appreciate any help received. Thanks.