Hi there, I'm new around here. I got this problem, I must demonstrate next limit by using the limits formal definition.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a_n= \displaystyle\frac{(-1)^n}{n^2}, L=2[/tex]

Which means:

[tex]\displaystyle\lim_{n \to{+}\infty}{\displaystyle\frac{(-1)^n}{n^2}}=2[/tex] (its a sequence, [tex]n\in{\mathbb{N}}[/tex]).

And I don't know how to solve this. Here is the formal definition of limit given on class:

[tex]\displaystyle\lim_{n \to{+}\infty}{a_n}=L\Leftrightarrow{\forall\epsilon>0\exists{n_0=n_0(\epsilon) \textsf{ such that } n\geq{n_0}\Rightarrow{|a_n-L|<\epsilon}}}[/tex]

I've tried to solve it, but couldn't find the way. I don't know how to solve [tex](-1)^n[/tex]. I actually thought at first sight that it didn't has a limit because of it, cause [tex](-1)^n[/tex] oscillates, but I actually don't know.

Thank you for reading. Bye bye.

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# Homework Help: Limits (formal definition)

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