Limit superior, sequence and series

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Can anyone tell me how to find limit superior of $\{(-1)^n/2^n : n = 1, 2, ... \}$

I separated the sequences and my answer is coming out to be 1/3. But options are $$ 1 \\ 0\\ -1 \\ 1/4 $$

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Guide:

The sequence converges, when a sequence converges, you just have to find its limit and it is equal to the limit superior.