(1-1/2)(1-1/3)(1-1/4)...(1-1/2008)

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(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2008)(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2008)(1-1/2)*(1-1/3)*(1-1/4)*

(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2008)
(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2008)

(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2008)
=1 / 2008