The Road to Reality
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Exercise [03.01]
http://www.roadtoreality.info/viewtopic.php?f=19&t=1632
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Author:  gandalf [ 27 Jul 2010, 19:16 ]
Post subject:  Exercise [03.01]

Since I found the numerical computations we are asked to do here rather annoying (calculating the approximation of order n doesnt help us anything in calculating the approximation of order n+1), I looked around a bit and found a recursion formula for continued fractions significantly simplifying these computations. Consequently, in my solution I first prove this recursion formula and then apply it to the numerical computations in question.

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