I'm studying up on data structures and algorithms via MIT 6.006. At one point, I got frustrated as to why there is no mechanical way of collapsing finite sums i

I'm studying up on data structures and algorithms via MIT 6.006. At one point, I got frustrated as to why there is no mechanical way of collapsing finite sums in their closed forms. Or how I used to say a couple of hours ago "create a formula out of those sums." So I looked some things up and this is a nice tutorial that I found on it. It's a bit crazy if you're not too mathematically inclined (like me, I know basic calculus), but it allowed me to kind of see that there is a system for creating closed forms out of certain finite sums. Two very new things you'll learn: 1. Falling powers (also called falling factorials). 2. Stirling numbers (and that they are useful for converting falling powers to the normal powers we're used to). edit: another good resource: http://faculty.cs.tamu.edu/klappi/csce411-s15/csce411-setFDCalculus.pdf http://faculty.cs.tamu.edu/klappi/csce411-s15/csce411-setFDC...