MTH 210 Midterm: MTH 210 Midterm 2005 Winter
Document Summary
This exam has 5 pages including this front page. It consists of 3 questions and is worth 25% of the course mark. Please answer all questions directly on this exam. One 8. 5" by 11" double-sided crib sheet is allowed, but no other aids are. If you need more room for the solutions, please continue on the back of the page and indicate. Question a recursion and induction 20 marks. Given the sequence an defined with the recurrence relation: a0 = 1 an = k (an-1)2 for n 1. Keep your intermediate answers as you will need them in the next question. Using iteration, solve the recurrence relation when n 1 (i. e. find an explicit formula for an). Your final solution can contain the symbols and . Show that 2 | n2 n for all positive integers n by weak induction. Question b number theory 20 marks. Use the euclidian algorithm to find gcd (598, 1287).
