Activity 8.1.3.
(a)
Recall our work with limits involving infinity earlier in the book. State clearly what it means for a continuous function \(f\) to have a limit \(L\) as \(x \to \infty\text{.}\)
(b)
Given that an infinite sequence of real numbers is a function from the integers to the real numbers, apply the idea from part (a) to explain what you think it means for a sequence \(\{s_n\}\) to have a limit as \(n \to \infty\text{.}\)
(c)
Based on your response to the part (b), decide if the sequence \(\left\{ \frac{1+n}{2+n}\right\}\) has a limit as \(n \to \infty\text{.}\) If so, what is the limit? If not, why not?
