Answer to Question #290052 in Real Analysis for Atharva

Question

Find the limit of the sequence section 3.2.6

Answer 1

$\displaystyle \text{Consider the sequence, $\frac{n-1}{n}$}\\ \lim_{n \to \infty}\frac{n-1}{n} = \lim_{n \to \infty} (1-\frac1n)\\ =\lim_{n \to \infty}1 - \lim_{n \to \infty} \frac1n\\ \text{Where $\lim_{n \to \infty} \frac1n = 0$}\\ \text{Hence,} \lim_{n \to \infty}\frac{n-1}{n}=1$