一道算术题.1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+...+1/98*99+1/99*100简便运算.

高丽华回答：

　　1/1*2+1/2*3+1/3*4+1/4*5+1/5*6……1/99*100=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)……+（1/99-1/100）=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6……+1/99-1/100中间那些可以对掉=1-1/100=99/100...