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I f a(n+1)=1/(1+1/(an)) , (n=1,2,3,4.......

I f `a_(n+1)=1/(1+1/(a_n)) , (n=1,2,3,4........2008)` and `a_1=1` the value of `a_1a_2+a_2a_3+a_3a_4+.............+a_(2008)a_(2009)=m` and `2009m=2^alpha*251^bbeta` then `alpha+beta=`

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