# 1mid245 - C ∪ B A ∩ C but that equality need not hold 3...

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Name: Midterm 1, Math 245 - Fall 2010 Duration: 50 minutes To get full credit you should explain your answers. 1. Prove that 1 1 + ··· + 1 n > 2 n + 1 - 2 for every natural number n 1. # Score 1 2 3 Total

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2. Let A,B,C be sets. Prove that ( A B ) \ C must be a subset of [ A \ ( B
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Unformatted text preview: C )] ∪ [ B \ ( A ∩ C )], but that equality need not hold. 3. Let ( a n ) n ≥ 1 be a sequence satisfying a 1 = a 2 = 1 and a n = a n-1 + 2 a n-2 2 for n ≥ 2. Show that 1 ≤ a n ≤ 2 for n ∈ N ....
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## This note was uploaded on 12/07/2011 for the course MATH 245 taught by Professor Cioaba during the Fall '10 term at University of Delaware.

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1mid245 - C ∪ B A ∩ C but that equality need not hold 3...

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