1 / 1 + 2 + 1 / 1 + 2 + 3 + 1 / 1 + 2 + 3 + 4 + ellipsis + 1 / 1 + 2 + ellipsis + 99

1 / 1 + 2 + 1 / 1 + 2 + 3 + 1 / 1 + 2 + 3 + 4 + ellipsis + 1 / 1 + 2 + ellipsis + 99

1+2+3+.+n=n(n+1)/2
1/(1+2+3+.+n)=2/[n(n+1)]=2[1/n-1/(n+1)]
Therefore, the above formula becomes
2/[1/2-1/3+1/3-1/4+.+1/99-1/100]
=2/(1/2-1/100)
=1-1/50
=0.98