When read Zorich's book Mathematical Analysis Vol I, I figure out a question concerning the Theorem 5, Page 133. That is:
Assuming function $f:(0,+\infty)\to\mathbb{R}, \text{ with } \lim\limits_{\mathbb{N}\ni n\to\infty} f(n)=A\in\mathbb{R}\cup\{+\infty,-\infty\},$ where $\mathbb{N}$ is the set of all positive integers. Is it true that $\lim_{x\to+\infty} f(x)=A$?
I guess that it may be true. But I am not so sure. Maybe it is just a corollary of Theorem 5, page 133 of Zorich's Book (see above). Can anyone help me? If it is false, give your counterexample, and if it is true, prove it. Thanks a lot!