(1-1/2*2)(1-1/3*3)(1-1/4*4).(1-1/2010*2010)(1-1/2011*2011)

(1-1/2*2)(1-1/3*3)(1-1/4*4).(1-1/2010*2010)(1-1/2011*2011)
(1-1/2*2)(1-1/3*3)(1-1/4*4).(1-1/2010*2010)(1-1/2011*2011)

(1-1/2*2)(1-1/3*3)(1-1/4*4).(1-1/2010*2010)(1-1/2011*2011)
原式=(1^2-(1/2)^2)(1^2-(1/3)^2)(1^2-(1/4)^2)...(1^2-(1/2010)^2)(1^2-(1/2011)^2)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(3/2)*(1/2)*(4/3)*(2/3)*(5/4)*(3/4)*...*(2011/2010)*(2009/2010)
=(1*2011)/(2*2010)
=2011/4020