Let {$a_n$} be a sequence of real numbers. Then what should be a necessary and sufficient condition for the existence of $\lim_{n\to\infty} a_n$?
P.S.- The condition should be in terms of existence of other limits, for example, it exists if $\lim_{n\to\infty} a_{2n}$ and $\lim_{n\to\infty} a_{3n}$ both exist, say...
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