题目

2/1*2+2/2*3+2/3*4+2/4*5+2/5*6+...+2/98*99+2/99*100

提问时间：2020-07-25

答案

原式=2×(1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...+1/98*99+1/99*100)
=2×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100)
=2×(1-1/100)
=2×99/100
=99/50