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extra-homework3

# extra-homework3 - e = exp(1 with the default precision then...

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Extra Problems for 1/9/09 1. Assume that u; v; w 2 Z , w > 0 and det ° u v w 1 ± = 1 . Show that if d is a positive integer that is not a square of an integer and p d = [ q 0 ; q 1 ; q 2 ; ::: ] is its simple continued fraction then u p d + v w p d + 1 = [ v; w; q 0 ; q 1 ; ::: ] : 2. Calculate the simple continued fraction for p 7 and for 3 p 7+2 p 7+1 check your work using pari. 3. Use Pari to calculate the simple continued fraction decomposition for
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Unformatted text preview: e = exp(1) with the default precision then set the precision to 50 ( n p 50) and 100. What would you guess is the partial fraction decomposition for e ? Try the same for & (Pi). Doyou see any pattern? 1...
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