A sequence Problem

Algebra Level 3

The sequence a1,a2,a3,a_1,a_2,a_3,\ldots satisfies an+2=2an+1+an,n=1,2,3,. a_{n+2}=\dfrac{2}{a_{n+1}}+a_n , \quad n=1,2,3,\ldots.

with initial values a1=1,a2=2a_1=1, a_2=2.

Find the value of a100×a101a_{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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