(1-1\2²)(1-1\3²)(1-1\4²).(1-1\2004²)(1-1\2005²)

问题描述:

(1-1\2²)(1-1\3²)(1-1\4²).(1-1\2004²)(1-1\2005²)
求这道算式的值(因式分解,

(1-1/2^2)(1-1/3^2)(1-1/4^2)…(1-1/2004^2)(1-1/2005^2)因为(1-1/2^2)=(2^2-1)/2^2=1/2*3/2(1-1/3^2)=(3^2-1)/3^2=2/3*4/3...(1-1/2005^2)=2004/2005*2006/2005故原式=(1/2*2/3*3/4...2004/2005)(3/2*4/3*...