prob5 - (b) Use part (a) to obtain the continued fraction...

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MATH 115B PROBLEM SET V MAY 17, 2007 (1) Compute the continued fraction expansion of: (a) 7; (b) (1 + 13) / 2. (2) Evaluate the following infinite simple continued fractions: (a) [ 2 , 3]; (b) [0; 1 , 2 , 3]. (3)(a) For any positive integer n , show that n 2 + 1 = [ n ; 2 n ], n 2 + 2 = [ n ; n, 2 n ] and n 2 + 2 n = [ n ; 1 , 2 n ]. [Hint: Notice that n + n 2 + 1 = 2 n + ( n 2 + 1 - n ) = 2 n + 1 n + n 2 + 1 . ]
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Unformatted text preview: (b) Use part (a) to obtain the continued fraction representations of 2, 3, 15 and 37. (4) Given the innite continued fraction [1; 3 , 1 , 5 , 1 , 7 , 1 , 9 ... ], nd the best rational ap-proximation a/b with (a) denominator b < 25; (b) denominator b < 225. 1...
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