Somewhere in between...

Algebra Level 5

Let a1>a2>0{ a }_{ 1 }>{ a }_{ 2 }>0 and an+1=(anan1){ a }_{ n+1 }=\sqrt { \left( { a }_{ n }{ a }_{ n-1 } \right) } ; n2n\ge 2. If limnan=la1ma2n\displaystyle{\lim_{ n\rightarrow \infty }{ a }_{ n }}=l{ a }_{ 1 }^{ m }{ a }_{ 2 }^{ n }, then what is the value of l+m+n?l+m+n?

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