请计算:1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+……+100)= .

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请计算:1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+……+100)= .

任意一项1/(1+2+3+…n)=2/n(n+1)=2[1/n -1/(n+1)]
1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+……+100)
=2(1-1/2+1/2-1/3+1/3-1/4+1/4+……+1/99-1/100+1/100-1/101)
=2(1-1/101)
=200/101