Problem 1 [55pts] (1) [25pts] Let P(n) be the statement that l + 2 + + n n(n +1)/2 , for every positive integer n. Answer the following (as part of a proof by weak mathematical induction) 1. [Spts] Define the statement P(1) 2. [5pts] Show that P() is True, completing the basis step 3. [10pts] Show that if P(k) is True then P(k+ is also True for k21, completing the induction step. 4. [5pts] Explain why the basis step and induction step together show that P(n) is True for each positive integer n