分子是1分母从1加到10+分子是1分母从1加到11+分子是1分母从1加到12.+分子是1分母从1加到20

1/(1+2+...+10)
=1/[(1+10)/2*10]
=1/(10*11/2)
=2*1/(10*11)
=2*(1/10-1/11)
1/(1+2+...+11)
=1/[(1+11)/2*11]
=1/[11*12/2)
=2*(1/11-1/12)
.
1/(1+2+...+20)
=2*(1/20-1/21)
原式
=2*(1/10-1/11+1/11-1/12+...+1/20-1/21)
=2*(1/10-1/21)
=2*11/210
=11/105