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Recursion Problem!
Let x_0 be a real number in the interval (0,1] and {x_n} be sequence for all n >= 0, defined inductively by setting x_n = sin(x_(n1)) for all n >= 1. I have already proved that {x_n} is a strictly decreasing sequence in (0,1] and that the lim x_n asn→∞ = 0.
We need to prove parts 2 and 3 in the attachment!Attachment 30204
Thanks!

Re: Recursion Problem!

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Re: Recursion Problem!
Hi,
A solution to the 2nd problem is just a lengthy application of L'hopital's rule. The attachment has most of the details:
Attachment 30208

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Re: Recursion Problem!
Hi again,
A "simpler" solution than my previous post is provided by the attachment. At least the derivatives involved are easily calculated.
Attachment 30212