4. Theses are two problems about familiar nite sums. n(n + 1) 2 . (Note: this question is not asking you to give the standard proof by mathematical induc- tion to verify the sum. Instead, it's asking you to actually deduce / explain the derivation of sum formula for p(n)). (a) Assume that Z k = p(n) where p is a quadratic polynomial. Show that p(n) = k=1 n(n + 1)(2n + 1) 6 . The \"Note\" in=Part (a) applies here too. You are to show how the formula for (101) can be deduced.) (b) Assume that Z k2 = q(n) where q is a cubic polynomial. Show that q(n) = k 1