lim n-> inf Xn=n^2/(n+1)-[n^2/(n+1)]

题目

lim n-> inf Xn=n^2/(n+1)-[n^2/(n+1)]
如标题.
求lim n-> inf Xn的值.
Xn = n^2/(n+1)-[n^2/(n+1)]
其中[ ] 的含义为取整.
inf 是无穷的意思.

答案

n^2/(n+1)=(n^2-1+1)/(n+1)=n-1+1/(n+1)
所以[n^2/(n+1)]=n-1
Xn=1/(n+1)
limXn=0