Lim n ^ 2 {(K / N) - (1 / N + 1) - (1 / N + 2) - (1 / N + k)} (where k is a constant independent of n)

Lim n ^ 2 {(K / N) - (1 / N + 1) - (1 / N + 2) - (1 / N + k)} (where k is a constant independent of n)

n^2{(k/n)-(1/n+1)-(1/n+2)-.-(1/n+k)}
=nn{(1/n-1/n+1)+(1/n-1/n+2)+…… +(1/n-1/n+k)}
=nn{1/n(n+1)+2/n(n+2)+…… +k/n(n+k)}
=n{1/(n+1)+2/(n+2)+…… +k/(n+k)}
lim(n{1/(n+1)+2/(n+2)+…… +k/(n+k)})
=
lim(n{1/(n+k)+2/(n+k)+…… +k/(n+k)})
=k(k+1)/2*lim(n/(n+k))
=k(k+1)/2
=>
lim n^2{(k/n)-(1/n+1)-(1/n+2)-.-(1/n+k)}
=k(k+1)/2