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Suppose (a_n} is a sequence such that the subsequences (a_2n-1) and (a_2n) converge to the same limit, say a. Show that (a_n} also converges

Suppose (a_n} is a sequence such that the subsequences (a_2n-1) and (a_2n) converge to the same limit, say a. Show that (a_n} also converges to a.

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