Principle of mathematical induction
Sequences, series and the binomial theorem · Mathematics
Study notes
Q: Prove by induction: 1 + 2 + ... + n = n(n+1)/2. Base: n = 1: LHS = 1, RHS = 1x2/2 = 1. True. Assume true for k: sum to k = k(k+1)/2. For k+1: sum = k(k+1)/2 + (k+1) = (k+1)(k/2 + 1) = (k+1)(k+2)/2. Matches formula at n = k+1. Done - true for all n.