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If I have a sequence defined as $a_n = (-1)^n + \frac{1}{n}$, how would I find the limit superior?

John Sawatzky
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    Look up an example of how lim sups are calculated. If you don't understand that example, go back to the definition of lim sup. This problem is pretty standard. – Yunus Syed Oct 07 '15 at 00:50

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Odd terms are non-positive, while even terms are greater than $1$. Hence the limit superior is also the limit superior of the even terms – which converge to $1$. Thus $$\limsup_{n\to\infty} a_n=1.$$

Bernard
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