Thomas' Calculus 13th Edition

sequence converges to $1$.
As we know that a sequence converges when $\lim\limits_{n \to \infty}a_n$ exists. Consider $a_n=1+\dfrac{(-1)^n}{n}$ Apply limits to both sides. $\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}[1+\dfrac{(-1)^n}{n}]$ $\lim\limits_{n \to \infty}a_n=[\lim\limits_{n \to \infty}1+\lim\limits_{n \to \infty}\dfrac{(-1)^n}{n}]$ $\lim\limits_{n \to \infty}a_n=1+\dfrac{1}{\infty}$ $\lim\limits_{n \to \infty}a_n=1+0$ $\lim\limits_{n \to \infty}a_n=1$ Hence, the sequence converges to $1$.