MATA31H3 Study Guide - Natural Number
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Please read the following statement and sign below: I understand that any breach of academic integrity is a violation of the code of behaviour on academic matters. By signing below, i pledge to abide by the code. Mata31h3 page 2 of 8 (1) (20 points) use induction to prove that n(cid:88) k=1. 4k is a fancy way of writing 41 + 42 + + 4n. ] n(cid:88) k=1. Thus, we see that whenever n a, we must have n + 1 a as well. By induction, we conclude that a = n, which is precisely what is claimed. (cid:3) (cid:110) n n : n(cid:88) Then from the de nition of a, k=1 k=1. Adding 4n+1 to both sides yields n+1(cid:88) k=1 n(cid:88) Midterm exam # 1 (2) (20 points) prove that. Then a z and b n such that a is fully reduced, Squaring both sides and simplifying shows that a2 = 5b2. In particular, a2 is a multiple of 5.
