(1-1/2²)(1-1/3²)(1-1/4²)·······(1-1/2007²)(1-1/2008²)快点要步骤谢谢

(1-1/2²)(1-1/3²)(1-1/4²)·······(1-1/2007²)(1-1/2008²)快点要步骤谢谢
(1-1/2²)(1-1/3²)(1-1/4²)·······(1-1/2007²)(1-1/2008²)
快点
要步骤
谢谢

(1-1/2²)(1-1/3²)(1-1/4²)·······(1-1/2007²)(1-1/2008²)快点要步骤谢谢
原式=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-/2008)
=3/2·1/2·4/3·2/3······2009/2008·2007/2008
=(1·2·3·3·4·4·······2007·2007·2008·2009）/(2·2·3·3······2007·2007·2008·2008）
=2009/4016

（1-1/2²）（1-1/3²）（1-1/4²）……（1-1/2007²）（1-1/2008²）
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/2007)(1+1/2007)(1-1/2008)(1+1/2008)
=1/2*3/2*2/3*4/3*3/4*5/4*...*2006/2007*2008/2007*2007/2008*2009/2008
=1/2*2009/2008
=2009/4016