Suppose (an) is Cauchy and that for every k ∈ N, the interval (−1/k, 1/k) contains at least one term of (an). Can we say that (an) converges to 0?  Either show that it does or give a counter-example.

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A: A detailed solution is given in Steps 2 and 3.

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Q: Suppose (an) is Cauchy and that for every k ∈ N, the interval (−1/k, 1/k) contains at least one term…

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Q: True or false? Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,1/n) contains…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.