Re: HSC 2013 3U Marathon Thread
2+10+60+...+(n^2 +1)n! = n(n+1)!
@n=1, lhs=rhs=2
assume true for n=k, (k^2 +1)k! = k(k+1)!
prove true fro n= k+1, k(k+1)! + (k^2 +2k+2)(k+1)! (from prev step)
= (k+1)!(k^2 +3k +2) = (k+2)(k+1)(k+1)!
RHS= (k+1)(k+2)! = (k+2)(k+1)(k+1)!