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Some recursive equation
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mot
Jul 8, 2009, 7:37:25 PM7/8/09
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Let 0<a<=1 and consider recursive equation x[n-1]*cosx[n]=x[n] with x
[0]=a.
I can prove that sequence (x[n]) belongs to interval (0,1] and limx[n]
=0. By numerical observation I think that x[n] is asymptotically equal
to 1/sqrt[n] i.e. lim(x[n]*sqrt[n])=1. It is true? How to prove it?
Thanks in advance!
[0]=a.
I can prove that sequence (x[n]) belongs to interval (0,1] and limx[n]
=0. By numerical observation I think that x[n] is asymptotically equal
to 1/sqrt[n] i.e. lim(x[n]*sqrt[n])=1. It is true? How to prove it?
Thanks in advance!
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