1\1+2+1\1+2+3+1\1+2+3+4+.1\1+2...20

1\1+2+1\1+2+3+1\1+2+3+4+.1\1+2...20
1\1+2+1\1+2+3+1\1+2+3+4+.1\1+2...20

1\1+2+1\1+2+3+1\1+2+3+4+.1\1+2...20
因为1+2+3+ …+n=n(n+1)/2
所以1/(1+2+3+ …+ n)=2[1/n-1/(n+1)]
所以1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+ …+1/(1+2+3+ …+n)
=1+2[1/2-1/3+1/3-1/4+1/4-1/5+1/n-1/(n+1)]
=1+2×[1/2-1/(n+1)]
=1+1-2/(n+1)
=2-2/(n+1)
=2n/(n+1)
将20带入,再减去1,等于19/21.