# Limit-o-saurus

Calculus Level 3

Let $$x_1,x_2,x_3,...x_n$$ be real numbers such that $$x_1> x_2 > x_3....>x_n$$.

Also $$x_1=\tan^{-1} {2}$$ and $$\sin (x_{n+1}-x_n)+\dfrac{1}{2^{n+1}} \sin(x_n) \sin(x_{n+1})=0$$ .

Let $$I= \lim _{ n\rightarrow \infty }{ \cot { x_n} }$$

Evaluate $$\large [ {I}]$$.

Note : [ ] represents the greatest integer function.

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