Answer
(a) See explanations.
(b) $0$
Work Step by Step
(a) $\lim_{n\to\infty}a_n=L$ means that the sequence will get arbitrarily close to $L$ with sufficiently larger $n$, and quantity $L$ is the limit of this convergent sequence. In other words, a convergent sequence will have a limit when the number $n$ approaches infinity.
(b) As $\lim_{n\to\infty}\frac{1}{n}=0$, and the term $(-1)^n$ will only change the sign of the result ($\pm0$), thus we have $\lim_{n\to\infty}\frac{(-1)^n}{n}=0$
