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(Solution Library) Prove that a sequence a_n does not converge to the number a if and only if there is some ε >0 and a subsequence a_n_k such that |a_n_k-a|≥

Question: Prove that a sequence \(\left\{ {{a}_{n}} \right\}\) does not converge to the number a if and only if there is some \(\varepsilon >0\) and a subsequence \(\left\{ {{a}_{{{n}_{k}}}} \right\}\) such that

\[|{{a}_{{{n}_{k}}}}-a|\ge \varepsilon \]

for every index k .

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Solution: The downloadable solution consists of 1 pages
Deliverable: Word Document


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