Answer to Question #113343 in Real Analysis for Awais

Question

Find limit of sequence =n+2/3-n

Answer 1

Let $(x_n)=\frac{n+2}{3-n}$ be a sequence in $\R$ .

$\therefore \lim_{n\to \infin} (x_n)=lim_{n\to \infin} \frac{n+2}{3-n}$

Divided numerator and denominator by n. We get

$$lim_{n\to \infin}(x_n)=lim_{n\to \infin} \frac{1+\frac{2}{n}}{\frac{3}{n}-1}$$

$=\frac{1}{-1}=-1$