Problem 1 Let T, and P be the nth triangular and pentagonal numbers, respectively. n(n+1) (a) Find a simple formula for P like the formula T Justify your answer. 2 (b) Make tables for T and Pr for 1≤ n ≤ 20. Find a pentagonal number other than 1 that is also a triangular number. (c) Prove that three times any pentagonal number is a triangular number. That is, prove that for every n, there is an m such that 3Pn = Tm-