21OMG just now i read Fixed point iteration, its exactly the same as i was thinking
This is created by me i am quite sure it is correct looking for a rigorous proof
Find the value of \lim_{n\rightarrow \infty}cos^{(n)}(t) where cos^{(1)}(x)= cos(x) , cos^{(n)}(x)= cos(cos^{(n-1)}(x))
n is a natural number and t is a real number.
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2 Answers
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262the answer will be the soln of the eqn -> cos x =x
since if this happens, then the sequence will become recurring give always the same answer .
the soln is somewhat around 0.74