A sequence Problem
Algebra
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.
by
Sandeep Bhardwaj