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I will explain in more detail.

I have been given the question;

The $n$th term of the sequence is given. Determine whether this sequence converges or diverges. If it converges, find its limit.

$$\frac{2}{(n^2+3)^{1/2}}$$

Now I'm not too worried about the answer, and more about the phrasing. If the question had stated limit with $n\rightarrow\infty$, I would be fine. But I am not comfortable with the wording and it threw me off. What should I be looking for if there is no stated limit? When we start with $0$, it gives a $\dfrac{2}{3^{1/2}}$ and with infinity, it converges to $0$. Does that mean the answer will be, converges to $0$?

And if the answer is infinity, should I say it diverges?

Thanks for the help!

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By "find its limit" they mean, find what it converges to--i.e., they mean the limit as $n \to \infty$. –  Goos Feb 12 at 2:49
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1 Answer 1

up vote 2 down vote accepted

The word "sequence" is the part that implies that "limit" means $\displaystyle \lim_{n\to\infty}$ and not, for example, $\displaystyle \lim_{n\to5}$.

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I see. So I substitute infinity in and if the answer is non-zero, that is the limit? And if it is zero, I have to do one of the limit tests? –  Pejman Poh Feb 12 at 3:01
    
If you find that the limit is $0$, then you're done, since the question is what the limit is. –  Michael Hardy Feb 12 at 17:26
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