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
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
答
(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)............(1+1/2009)(1-1/2009)(1+1/2010)(1-1/2010)
=(3/2)(1/2)(4/3)(2/3)................(2010/2009)(2008/2009)(2011/2010)(2009/2010)
=(1/2)(2011/2010)
=2011/4020
答
1/2*(......)*(1+1/2010)
=2011/4020
答
(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