1/(23)+1/(34)+1/(45)+...+1/(9899)+1/(99*100)等于多少请解释为什么

来源：学生作业帮助网编辑：作业帮时间：2024/05/14 20:09:33

1/(2*3)+1/(3*4)+1/(4*5)+...+1/(98*99)+1/(99*100)等于多少请解释为什么
1/(2*3)+1/(3*4)+1/(4*5)+...+1/(98*99)+1/(99*100)等于多少
请解释为什么

1/(2*3)+1/(3*4)+1/(4*5)+...+1/(98*99)+1/(99*100)等于多少请解释为什么
1/(2*3)+1/(3*4)+1/(4*5)+...+1/(98*99)+1/(99*100)
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100
=1/2-1/100
=49/100

1/2-1/100=49/100

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