1/1*2+1/2*3+1/3*4+……+1/n(n+1)=?
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1/1*2+1/2*3+1/3*4+……+1/n(n+1)=?
![1/1*2+1/2*3+1/3*4+……+1/n(n+1)=?](/uploads/image/z/18827732-20-2.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B%E2%80%A6%E2%80%A6%2B1%2Fn%EF%BC%88n%2B1%EF%BC%89%3D%3F)
1/1*2+1/2*3+1/3*4+...+1/n(n+1)
=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-1/(n+1)
=1-1/(n+1)
=(n+1-1)/(n+1)
=n/(n+1)
=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-1/(n+1)
=1-1/(n+1)
=(n+1-1)/(n+1)
=n/(n+1)
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