Subsequences of a sequence of real numbers, Subsequential limits, The limit superior
(or upper limit), The limit inferior (or
lower limit), Bolzano-Weierstrass Theorem, A sequence is convergent if and only if all of its subsequences converge to the same limit.
For all the lectures on Calculus, follow the link:
https://www.youtube.com/playlist?list=PLY2U8CcmALO4g0zdxohOzUmMlv04Z9kGD