1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4)……+1/(1+2+3+4+……+99+100)=( )
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![1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4)……+1/(1+2+3+4+……+99+100)=( )](/uploads/image/z/8572359-39-9.jpg?t=1%2F%281%2B2%29+%2B+1%2F%281%2B2%2B3%29+%2B+1%2F%281%2B2%2B3%2B4%29%E2%80%A6%E2%80%A6%2B1%2F%EF%BC%881%2B2%2B3%2B4%2B%E2%80%A6%E2%80%A6%2B99%2B100%EF%BC%89%3D%EF%BC%88+%EF%BC%89)
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1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4)……+1/(1+2+3+4+……+99+100)=( )
1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4)……+1/(1+2+3+4+……+99+100)=( )
1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4)……+1/(1+2+3+4+……+99+100)=( )
1+2+3+...+n=n(n+1)/2 1/(1+2+3+...+n)=2/n(n+1)=2(1/n-1/(n+1)) 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4)……+1/(1+2+3+4+……+99+100) =2*[1/2-1/3+1/3-1/4+...+1/100-1/101] =2*(1/2-1/101) =99/101.