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$a_n = \{1/2, -1/2, 3/4, -3/4, 7/8, -7/8, .......\}$

The definition I am trying to relate this question to is

$ <x_n>$ is a sequence, $<x_{n_k}>$ is the subsequence of $<x_n>$.

$<x_{n_k}$ converges to x. x is the subsequential limit.

I find the task of identifying a subsequence confusing.

Would it suffice to make

positive values =p negative values = n

$\{ a_{n_p} \} = \{ 1/2, 3/4, 7/8... \}$

$\{ a_{n_n} \} = \{ -1/2, -3/4 -7/8... \}$

both converge to 0. then does this demonstrate the subsequential limit is 0?

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If you take the odd elements of the sequence as a subsequence then this subsequence will converge to 1. The even subsequence will converge to -1

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