1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,
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1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,
首先:1+2+3+4+…+n=n(n+1)/2
∴原式=2/(2*3)+2/(3*4)+2/(4*5)+…+2/(n(n+1))
=2(1/2-1/3+1/3-1/4+1/4-1/5+…+1/n-1/(n+1))
=2(1/2-1/(n+1))
=(n-1)/(n+1)