(1-1/2²)(1-1/3²)×……×(1-1/2011²)(1-1/2012²)要有过程和理由解释.

问题描述:

(1-1/2²)(1-1/3²)×……×(1-1/2011²)(1-1/2012²)要有过程和理由解释.
有满意答案会额外给50分.

(1-1/2²)(1-1/3²)×……×(1-1/2011²)(1-1/2012²)=(1+1/2)(1-1/2)(1+1/3)(1-1/3)x...x(1+1/2011)(1-1/2011)(1+1/2012)(1-1/2012)=3/2x1/2x4/3x2/3x...2012/2011x2010/2011x2013...