用简便方法计算:(1/2-1)+(1/3-1/2)+(1/4-1/3)+...+(1/100-1/99)这道题请求帮助,.
问题描述：
用简便方法计算:(1/2-1)+(1/3-1/2)+(1/4-1/3)+...+(1/100-1/99)这道题请求帮助,.
答
(1/2-1)+(1/3-1/2)+(1/4-1/3)+...+(1/100-1/99) 去括号,移项
=-1+1/2-1/2+1/3-1/3+1/4-1/4+……-1/99+1/100
=-1+1/100
=-99/100