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Unformatted text preview: F 1 = 1, F 2 = 1, and for n 3, F n = F n-1 + F n-2 ). Prove that F n 2 + F n +1 2 = F 2 n +1 for all n 1. 4: Find the number of ways to roll six identical 6-sided dice (one such way is to roll two 3s, three 5s and one 6). 5: Let a = 9 and for n 0 let a n +1 = 3 a n 4 + 4 a n 3 . Prove that for all n 0, at least 2 n of the digits in a n are nines. 6: There are n points on a circle. Each pair of points is connected by a line segment. No three of these line segments meet at a point. Find the number of regions into which the circle is divided....
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- Fall '08