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,.

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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,.
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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,.
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,.

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,.
(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