- #1
davitykale
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Homework Statement
Prove that lim a_n = L given that (a_n) is a sequence defined such that every subsequence has a convergent that converges to L\in R
Homework Equations
Bolzano-weierstrass and the works
The Attempt at a Solution
A subsequence of a subsequence is just a subsequence of the original sequence, so if I can show that (a_n) is bounded. Can I do something with maybe 2L as a bound?