Q1 (15 points) Consider the following 12 + 23 + 32 + ... + ( 37 ) ? (a)[1 point] Turn the given sum into sigma notation. (b)[2 points] Use the sigma identities to show that 12 + 22 + 32 + ...+ (3n)2 n(3n + 1) (6n + 1) 2 (c)[12 points] Use the principle of mathematical induction to prove that 12 + 22 + 32 + ... + (372) ? n(3n + 1) (6n + 1) 2