I was having a debate with a friend about how to show the following limit.(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \lim_{n \to \infty} \cos( \frac{2 \pi}{2n - 2} )^n = 1 [/tex]

I claim that you can just hand-wavingly say that since cosine of 0 is 1, and 1^infinity is 1, the limit is 1. He claims I need to show this using some sort of limit theorem (I don't want to get into delta-epsilons).

Is there a cool limit theorem I can use?I

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# An interesting limit

**Physics Forums | Science Articles, Homework Help, Discussion**