1st CaMO 1969 Problem 6 Find 1.1! + 2.2! + ... + n.n! .
We show by induction that 1·1! + 2·2! + ... + n·n! = (n+1)! - 1. It is obviously true for n = 1. Suppose it is true for n, then 1.1! + ... + (n+1) (n+1)! = (n+1)! - 1 + (n+1) (n+1)! = (n+2)! - 1, so it is true for n+1. 1st CaMO 1969 © John Scholes jscholes@kalva.demon.co.uk 10 June 2002