lim(n趋向于无穷)(k/n-1/n+1-1/n+2-‘‘‘‘-1/n+k)(其中K为与N无关的正整数)
问题描述:
lim(n趋向于无穷)(k/n-1/n+1-1/n+2-‘‘‘‘-1/n+k)(其中K为与N无关的正整数)
答
=lim(1/n-1/(n+1)+1/n-1/(n+2)+...+1/n-1/(n+k))
=lim(1/(n+1)+2/(n+2)+...+k/(n+k))/n
lim(1/(n+1)+2/(n+2)+...+k/(n+k))/n>=lim(1/(n+1)+1/(n+2)+...+1/(n+k))/n>=lim(1/(n+k)+1/(n+k)+...+1/(n+k))/n=lim k/(n(n+k))=0
lim(1/(n+1)+2/(n+2)+...+k/(n+k))/n