Use mathematical induction to prove the following statements. a) 1 + 3 + 6 + ... + n(n + 1)/2 = n(n + 1)(n + 2)/6 b) 1^3 + 2^3 + ... + n^3 = n^2(n + 1)^2/4 c) 3^2 + 6^2 + 9^2 + ... + (3n)^2 = 3n(n + 1)(2n + 1)/2 d) 1 middot 2 middot 3 + 2 middot 3 middot 4 + ... + n(n + 1)(n + 2) = n(n + 1)(n + 2)(n + 3)/4 e) 1/1 middot 3 + 1/3 middot 5 + 1/5 middot 7 + ... + 1/(2n - 1) (2n + 1) = n/2n + 1