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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.


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 $n \to \infty$. – 6005 Feb 12 '14 at 2:49
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 '14 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 '14 at 17:26

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