Prove that every bounded increasing sequence is convergent

Question

Kaitlyn Heath

Mathematics

16 January, 04:05

Prove that every bounded increasing sequence is convergent

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Kassandra Gates · Answer 1

The proof of this can be get with a slight modification. It can be prove that every bounded is convergent, If (an) is an increasing and bounded sequence, then limn → ∞an = sup{an:n∈N} and if (an) is a decreasing and bounded sequence, then limn→∞an = inf{an:n∈N}.