The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.
What is Bolzano-Weierstrass Theorem?
The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.
According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.
***See proof in the attached document.
Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.
Learn more about Bolzano-Weierstrass Theorem:
https://brainly.com/question/1581408
#SPJ1
