Consider the sequence ${x_n}$ defined by $x_n = [nx]/
n$ for $x\in\mathbb R$ where $[·]$ denotes the integer part. Then ${x_n}$
(a) converges to $x$.
(b) converges but not to $x$.
(c) does not converge
(d) oscillates.
I think (a) is correct as $\lim_{n \to \infty}[n]/n=1$. Am I right?