1 votes 1 votes Consider the sequence $\left \{x_{n} \right \}$ defined by $x_{n}=\frac{\left[nx\right]}{n}$ for $x \in \mathbb{R}$ where $[·]$ denotes the integer part. Then $\left \{x_{n} \right \}$ Converges to $x.$ Converges but not to $x.$ Does not converge Oscillates Set Theory & Algebra tifrmaths2011 convergence + – makhdoom ghaya asked Dec 9, 2015 edited Aug 18, 2020 by soujanyareddy13 makhdoom ghaya 591 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Oscillates Abhishek rai 1 answered Sep 28, 2017 Abhishek rai 1 comment Share Follow See all 2 Comments See all 2 2 Comments reply Rohit Gupta 8 commented Sep 28, 2017 reply Follow Share Explanation Please. 0 votes 0 votes Royari commented Dec 2, 2017 reply Follow Share Wrong Answer 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes We know that $n<x<n+1$Where $n\in \mathbb{N}$ then $[x]=n$So $nx-1< [nx]\le nx \Rightarrow x-\frac{1}{n}<\frac{[x]}{n}\le x$ Now by Sandwitch therem limit is $x$ Royari answered Dec 2, 2017 Royari comment Share Follow See all 0 reply Please log in or register to add a comment.