Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

This is from so called ratio test, which says

The series Ʃa(n) diverges if abs{a(n+1)/a(n)} ≥ 1 for n≥N where N is some fixed integer.

I was wondering if I could replace the condition with lim inf abs{a(n+1)/a(n)} ≥ 1.

So basically what I'm asking is whether these two below are equivalent or not.

1. abs{a(n+1)/a(n)} ≥ 1 for n≥N where N is some fixed integer

2. lim inf abs{a(n+1)/a(n)} ≥ 1

*a(n) means nth term in the sequence, and abs means absolute value.

Thank you in advance.

**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!

# Could you check if these two are equivalent?

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