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math104b-extraprobs-2-02

math104b-extraprobs-2-02 - 1351 780 and the n 2...

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Extra Exercises for 2/2/09 references to pari are to the program gp.exe that will be available when the program is installed. 1. Calculate the continued fraction expansion of p 3 assertion 265 153 < p 3 < 1351 780 as convergents. Show that if 265 153 is the n th convergent then the n +1 convergent C n +1 p 3 < C n +1 <
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Unformatted text preview: 1351 780 and the n +2 satis&es 265 153 < C n +2 < p 3 . Can you think of a reason why Archimedes used the choices above? 2. Use Pari to calculate the &rst 4 convergents of & (Pi in Pari). Use Pari to &nd the decimal expansions of these convergents (if you enter 22.0/7 you will get the decimal expansion). 3. Calculate by hand the continued fraction decomposition of a) 2813/113 b) 2701/409. Show your work and check using Pari gp. 1...
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