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Problem 1 148pts] (1) I 10pts! 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. [2pts] Define the statement P(1) 2. [2pts] Show that P(1 is True, completing the basis step. 3. [4pts] Show that if P(k) is True then P(k+1 is also True for k1, completing the induction step. [2pts] Explain why the basis step and induction step together show that P(n) is True for all n. 4. (2) [15ptsl Using (weak) mathematical induction, prove that n2 1 is an odd positive integer, where n is a positive integer. Show all steps involved in the proof.

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