计算:(1/50-1)*(1/49-1)*(1/48-1)*...*(1/4-1)*(1/3-1)

问题描述:

计算:(1/50-1)*(1/49-1)*(1/48-1)*...*(1/4-1)*(1/3-1)

(1/50-1)*(1/49-1)*(1/48-1)*...*(1/4-1)*(1/3-1)*(1/2-1)
=(-49)/50*(-48)/49*(-48)/47*...*(-3)/4*(-2)/3*(-1)/2
=-1/50(有49个负数相乘,故为负)
(前一个分数的分子与后一个数的分母相同,故可以约掉)