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Let a(1),a(2),a(n) be sequence of real n...

Let `a_(1),a_(2),a_(n)` be sequence of real numbers with `a_(n+1)=a_(n)+sqrt(1+a_(n)^(2))` and `a_(0)=1`. Prove that `lim_(xtooo)((a_(n))/(2^(n)))=4/(pi)`

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The correct Answer is:
`=4/(pi)`
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