Just something I thought was interesting:

I was playing around with summations and integrals, especially summations. I was looking at the summation from n=1 to infinity of n^y x^(n-1). I was testing out if I could solve it for difference values of y, assuming |x|<1, and I got to a recursive way to solve it. The summation, I’ll call it A(x,y), equals A(x,y-1)+x*d/dx(A(x,y-1)). Just cool I thought.