limn→∞(n^2)*(k/n -1/(n+1)-1/(n+2)...-1/(n+k)
=limn→∞(n^2)*k/n -limn→∞(1/(n+1)+1/(n+2)...+1/(n+k))
其中：当N→-∞或→+∞时,1/(n+1)+1/(n+2)+.+1/(n+k)的极限→0
所以：limn→∞(n^2)*(k/n -1/(n+1)-1/(n+2)...-1/(n+k)
＝limn→∞(nk)
=∞