assume an is a bounded sequence with the property thatevery convergent subsequence of an converg

Name: assume an is a bounded sequence with the property thatevery convergent subsequence of an converges to the same limit a r show that an must converge to a 04268
Uploaded: 2023-03-28T16:04:38-08:00
Duration: 3 min 12 s
Channel: Sri K
Description: assume an is a bounded sequence with the property thatevery convergent subsequence of an converges to the same limit a r show that an must converge to a 04268

Question

William Semus · Accepted Answer

1. Since $(a_n)$ is a bounded sequence, by the Bolzano-Weierstrass theorem, it has a convergent

Question

Assume (an) is a bounded sequence with the property thatevery convergent subsequence of (an) converges to the same limit a ∈ R. Show that (an) must converge to a.

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