If a sequence is convergent, then the sequence is Cauchy. O A. True OB. False

Question

Mathematics

Mina Sosa

27 October, 07:04

If a sequence is convergent, then the sequence is Cauchy. O A. True OB. False

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Answers (1)

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Anastasia Santiago · Answer 1

Answer: True

Explanation:

Yes, the given statement is true that the if the sequence is convergent then the given sequence is always Cauchy. The every cauchy sequence should be bounded because due to the complete space metric in the triangle inequality. So that is why, the cauchy sequence is always convergent.

In the mathematics, cauchy sequence are those sequence whose element are arbitrarily closed to one another.