Hi all, my task is to check, whether the given sequence has a limit and if yes, count it. We have to do it using the definition of limit.(adsbygoogle = window.adsbygoogle || []).push({});

So I have eg. this sequence:

[tex]

(-1)^n \left( \frac{1}{10} - \frac{1}{n} \right)

[/tex]

I know how the definition is, but I don't know how to use it for the purpose wanted. I just wrote

[tex]

\left| A - (-1)^n \left( \frac{1}{10} - \frac{1}{n} \right) \right| < \epsilon , \forall \epsilon > 0

[/tex]

But how to prove that the sequence has or has not limit? Should I just try to prove existence of the limit, or, on the contrary, should I try to prove that the limit doesn't exist? What is the general recommended method, when we have to prove it from definition of limit?

Thank you all for any answer.

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# Use definition of limit

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