- #1
twoflower
- 368
- 0
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.
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.
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.