- #1

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## Homework Statement

Here is a worked example:

http://img79.imageshack.us/img79/1909/88760168.gif [Broken]

I don't understand why they used the "limit comparison test" and not the "comparison test".

Why can't we just conclude that the series [tex]\sum^{\infty}_{n=1} (\frac{n+1}{n^2 +1})^3[/tex] converges by comparison with [tex]\frac{1}{n^3}[/tex]?

What's the necessity of using the limit comparison test?

Furthermore, I would like to know in which cases it is more suitable to use the comparison test and when to use the limit comparison test. I appreciate some guidance here. Thanks.

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