# Homework Help: Ratio Test - Lim sup and lim inf version -

1. Mar 19, 2010

### michonamona

Hello friends,

1. The problem statement, all variables and given/known data
$$lim sup |\frac{a_{n+1}}{a_{n}}|$$

I know that this operation tests for convergence, but I don't understand how it's related to $$lim_{n -> \infty}|\frac{a_{n+1}}{a_{n}}|$$

I understand that both will give the same result, but how is the latter different? lim sup is the sup of the collection of sub-sequential limits, so what does it mean when we take $$lim sup |\frac{a_{n+1}}{a_{n}}|$$ ?

I appreciate your help,

M

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