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.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Use definition of limit

Loading...

Similar Threads for definition limit | Date |
---|---|

B Question about a limit definition | Feb 27, 2018 |

I Question about Complex limits of definite integrals | Jan 30, 2017 |

I Epsilon in the limit definition | Jan 13, 2017 |

B Definition of the limit of a sequence | Jul 27, 2016 |

B Definition of limit problem | Jun 14, 2016 |

**Physics Forums - The Fusion of Science and Community**