prob5

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

This preview shows page 1. Sign up to view the full content.

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 . ]
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (b) Use part (a) to obtain the continued fraction representations of √ 2, √ 3, √ 15 and √ 37. (4) Given the inﬁnite continued fraction [1; 3 , 1 , 5 , 1 , 7 , 1 , 9 ... ], ﬁnd the best rational ap-proximation a/b with (a) denominator b < 25; (b) denominator b < 225. 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online