(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)用因式分解计算,上面那个是平方rt,求做
问题描述：
(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)用因式分解计算,上面那个是平方
rt,求做
答
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/10)(1+1/10)
=(1/2)[(3/2)(2/3)(4/3)(3/4)(5/4).(8/9)(10/9)(9/10)](11/10)
=(1/2)x1x1x1.x1x(11/10)
=(1/2)(11/10)
=11/20