Answer
7a. $\displaystyle\lim_{n\to\infty} a_{n} = L$ means that given a large enough $n$, the $n$th term of the sequence will approach $L$.
7b. $0$
Work Step by Step
7a. This is the definition of a limit, combined with the context of this problem being a convergent sequence. $\displaystyle\lim_{n\to\infty} a_{n} = L$ means that given a large enough $n$, the $n$th term of the sequence will approach $L$.
7b. $\displaystyle\lim_{n\to\infty} \frac{(-1)^n}{n}$ is a function such that the denominator gets infinitely large, while the numerator oscillates between $-1$ and $1$. Therefore, the fraction gets smaller over time (larger denominator), and as $n$ approaches infinity, the fraction will approach $0$.
