计算:(1-2²分之1)(1-3²分之1)(1-4²分之1)...(1-9²分之1)
问题描述：
计算:(1-2²分之1)(1-3²分之1)(1-4²分之1)...(1-9²分之1)
答
利用平方差公式即可
(1-2²分之1)(1-3²分之1)(1-4²分之1)...(1-9²分之1)
=(1-1/2)(1+1/2)*(1-1/3)*(1+1/3)*(1-1/4)(1+1/4)*.*(1-1/9)*(1+1/9)
= (1/2)*(3/2)* (2/3)*(4/3) *(3/4)*(5/4)*.*(8/9)*(10/9)
=(1/2)*(10/9)
=5/9