1980/(1*2*3)+1980/(2*3*4)+1980/(3*4*5)+.1980/(98*99*100)=?_数学解答

1980/(1*2*3)+1980/(2*3*4)+1980/(3*4*5)+.1980/(98*99*100)=?

人气：416 ℃　时间：2019-10-19 16:11:48

解答

原式=1980/2*(1/1-2/2+1/3+1/2-2/3+1/4+1/3-2/4+1/5+...1/98-2/99+1/100)
=1980/2*(1+1/2-1/99+1/100)
=14849/10