Unformatted text preview: + 3 x 33 x 211 x6 , 2 x 4 + 13 x 3 + 28 x 2 + 23 x + 6). 13. For any n ≥ 1 1 + 7 + 19 + ... + (3( n1)( n2) + 1) + (3 n ( n1) + 1) = n 3 14. a For any n ≥ 1, prove that 2 n +2 does divide 3 2 n1. (only one of (x1),(x+1) can be divisible by four at the same time, if one is even both are even) 14. b For any n ≥ 1, prove that 2 n +3 does not divide 3 2 n1. (Easy ±rst case, use the last problem to build up to this one.) 15. Expand the ±rst 3 terms of (2 x + 3) 15 . 16. How many ways are there to pick 8 books from 10 and put them in order on the bookshelf?...
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 Fall '10
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 Linear Algebra, Algebra, Division, Complex number, Easy ﬁrst case

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