观察式子(1-1/2²)(1-1/3²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)=1/2x3/2x2/3x4/3=2/3试求

问题描述:

观察式子(1-1/2²)(1-1/3²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)=1/2x3/2x2/3x4/3=2/3试求
试求(1-1/2²)(1-1/3²)x…x(1-1/2009²)(1-1/2010²)的值

(1-1/2²)(1-1/3²)x…x(1-1/2009²)(1-1/2010²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)x……x(1-1/2010)(1+1/2010)=1/2x3/2x2/3x4/3x……x2011/2010=1/2x2011/2010=2011/4020