MATH 4200 Midterm: MATH 4200 LSU Fall 12 Exam 1a
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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. Reverse the above calculations to write as a linear combination: = 63 (231 3 63) = 4 525 9 231. Thus 21 = 4 525 9 231: [18 points] use induction to prove that the equation. 1 + 3 + 5 + + (2 1) = 2 is valid for all integers 1. That is, the sum of the rst odd integers is equal to 2. Let () be the statement 1 + 3 + 5 + + (2 1) = 2 . Then (1) is the statement 1 = 12 , which is true. 1 + 3 + 5 + + (2 1) = 2 . 1 + 3 + 5 + + (2 1) + (2( + 1) 1) = 2 + 2 + 1.
