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The sequence a1,a2,a3,…a_1,a_2,a_3,\ldotsa1,a2,a3,… 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.an+2=an+12+an,n=1,2,3,….
with initial values a1=1,a2=2a_1=1, a_2=2a1=1,a2=2.
Find the value of a100×a101a_{100}\times a_{101}a100×a101.
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