...I'm back. And I passed that fucking PDEs exam! You guys. I'm nearly finished with this degree. But before I do. Can anyone help with some...uhhh...probably comes under the heading of graph theory, though is mostly just manipulation of summations. I can't grasp it, conceptually. Question: Solution: The crucial step I don't understand is how the third expression in the solution equates to the fourth. Though additionally if anyone has any resources for improving understanding of summation notation, that'd be aces. I find it unintuitive. Edit: 10 mins of scribbling & staring into space later...I've verified that both expressions are accurate, but I'm still stuck on how to manipulate the summations algebraically. Man, this field is so cool. I wish I understood it.