A sequence Problem

Calculus Level 3

The sequence \(a_1,a_2,a_3,\ldots\) satisfies \[ a_{n+2}=\dfrac{2}{a_{n+1}}+a_n , \quad n=1,2,3,\ldots .\]

with initial values \(a_1=1, a_2=2\).

Find the value of \(a_{100}\times a_{101}\).


You can try my other Sequences And Series problems by clicking here : Part II and here : Part I.
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