I'm trying to get some extra practice in before my final exam in two weeks and I ran across this problem. How can we do it?
Part A: Suppose for some $ b>0, f: [b, \infty ) \rightarrow R$ is such that $\lim_{x\to \infty} f(x) = L$ for some real number $L$. Let $a_n = f(n)$ for all integers $n>b$. Show that we also have $\lim_{n\to \infty} a_n = L$.
Part B: Give an example to that the converse to the result in part (a) is not true.