# Sequences and series

1. Feb 8, 2009

### arctic_girl4

How do you know if a sequence converges or diverges based on taking the limit?

here's an example
f:= 3^n/n^3;

if i take the limit the sequence goes to infinity.

does it diverge becuase the limit is not zero or can the limit be something other than zero and it still converge?

2. Feb 8, 2009

### HallsofIvy

Staff Emeritus
You are talking about a sequences and not series? You titled this "sequences and series". There is a theorem that says that if a sequence does not converge to 0, then the series (infinite sum) of those numbers cannot converge but certainly if a sequence converges to any number then it converges!

However in this case the sequence "goes to" infinity, as you say, and infinity is not a number. The sequence diverges. Many textbooks would say this sequence "diverges to infinity".