MATH 4023 Midterm: MATH 4023 LSU 4023s08 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. Solution. s2 = 2s1 + 3 = 2 5 + 3 = 13; s3 = 2s2 + 3 = 2 13 + 3 = 29; s4 = 2s3 + 3 = 2 29 + 3 = 61. (b) using mathematical induction, show that sn = 2n+2 3 for all positive integers n p. Your proof should be written in grammatically correct complete sentences. You should be explicit in stating what is your induction hypothesis and where you are using it. For n p, let p (n) be the statement sn = 2n+2 3. since s1 = 5 = 21+2 3, it follows that p (1) is true, which establishes the base step for induction.
