利用乘法公式计算(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)...(1-1/2005²)

(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)...(1-1/2005²) =(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/2005)(1+1/2005)=1/2*3/2*2/3*4/3*.*2004/2005*2006/2005=1/2*2006/2005=1003/2005