MATH 4023 Midterm: MATH 4023 LSU 4023s04 Exam fa
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Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each page of your paper: [15 points] prove that the formula. 2n is valid for all integers n 2. Your proof should be written in grammatically correct complete sentences. For n p, let p (n) be the statement: For n = 2, p (2) is the statement: Thus p (2) is true, and the base step for induction is veri ed. Now assume that p (k) is true for some xed k 2. Consider the left hand side of the statement p (n) for n = k + 1. Because of the assumption that p (k) is true, ( ) can be written as. 2k (k + 1)2 1 (k + 1)2 .
