1/(1+2+3+..+n)=2/n(n+1)
1+1/(1+2)+1/(1+2+3)+..+1/(1+2+..+n)
=2/1*2+2/2*3+2/3*4+2/4*5+..+2/n(n+1)
=2(1-1/2+1/2-1/3+1/3-1/4+..+1/n-1/(n+1)
=2(1-1/(n+1)
=2n/(n+1)