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        riddles >> medium >> Trignometric Recurrence
        
(Message started by: ThudanBlunder on Aug 1st, 2010, 12:41pm)
Title: Trignometric Recurrence
Post by ThudanBlunder on Aug 1st, 2010, 12:41pm
If u1 = 1 and un+1 = cos[arctan(un)] for n http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/geqslant.gif 1, find a formula for un.
Title: Re: Trignometric Recurrence
Post by towr on Aug 1st, 2010, 1:45pm
[hide]Using cos(atan(x)) = 1/sqrt(x2+1)
Take vn = u2n
Then vn+1 = 1/(vn + 1)  => convergents for phi-1
In other words, vn+1 = F(n)/F(n+1)
So, un = sqrt( F(n)/F(n+1) )
[/hide]


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