I have this problem that I could not solve, so I looked up the answer. It more of less said how we had to start to get to the answer. So I try that and get the right answer, but I still don't understand what this first step MEANS.(adsbygoogle = window.adsbygoogle || []).push({});

The question is about sequences and it says: Find an interval which contains all terms but the first 20 of the sequence defined by

[tex]x_n =4+\frac{(-1)^n}{n}[/tex]

If we start by saying "we are looking for an [itex]\epsilon>0[/itex] such that [itex]\forall n>20[/itex], [itex]|x_n - 4|<\epsilon[/itex]", everything follows very smoothly and we find that this epsilon is 1/20 and that the interval is (3+19/20 , 4+1/20).

But this "we are looking for an [itex]\epsilon>0[/itex] such that..." begining is not the real begining, because what we are looking for really is an INTERVAL. An interval [itex]I[/itex] such that [itex]\forall n>20[/itex], [itex]x_n \in I[/itex]. So how do the "we are looking for an [itex]\epsilon>0[/itex] such that..." follows from the real question that is asked?

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# Why do I get the right answer?

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