(1-1/2^2)*(1-1/3^2)*...*(1-1/2009^2)*(1-1/2010^2)=

问题描述:

(1-1/2^2)*(1-1/3^2)*...*(1-1/2009^2)*(1-1/2010^2)=

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