- #1
michonamona
- 122
- 0
Hello friends,
[tex] lim sup |\frac{a_{n+1}}{a_{n}}|[/tex]
I know that this operation tests for convergence, but I don't understand how it's related to [tex] lim_{n -> \infty}|\frac{a_{n+1}}{a_{n}}|[/tex]
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 [tex] lim sup |\frac{a_{n+1}}{a_{n}}|[/tex] ?I appreciate your help,
M
Homework Statement
[tex] lim sup |\frac{a_{n+1}}{a_{n}}|[/tex]
I know that this operation tests for convergence, but I don't understand how it's related to [tex] lim_{n -> \infty}|\frac{a_{n+1}}{a_{n}}|[/tex]
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 [tex] lim sup |\frac{a_{n+1}}{a_{n}}|[/tex] ?I appreciate your help,
M