About the binomial theorem. When we did this in class, our teacher wanted us to find the coefficient of the Nth term, and I could find it really quickly in my head, which greatly impressed him. He gave us three middle coefficients of (x+y)^8 (hence showing 3,4,5 choose 8) and wanted us to compute the middle coefficient of (x+y)^9 (4 or 5 choose 9). This is simple: C(n,k+1) = C(n,k) * (n-k) / (k+1).
19 November 2021
