How did Euler came up with a solution of 1/4 for the series 1-2+3-4.... There is a wikipedia page explaining it, http://en.wikipedia.org/wiki/1_−_2_+_3_−_4_+_·_·_· but I'm not quite following the manipulation of the numbers. How is a 1 pulled out and everything else goes to 0? It just doesn't make any sense to me. Also how is it that a divergent series can equal a single number? Is that not the definition of convergence? To go to a single number? What is up with this? Thanks a lot!