MHB Determining convergence/divergence

[ineedhelpnow]

what's the easiest way to quickly determine convergence or divergence? or is there a way to do it by calculator? i have a test today and most of the questions ill be given a series (few sequences) and itll be asking whether they converge or diverge?

 

[MarkFL]

If you can show that:

$$\lim_{n\to\infty}a_n=L$$

where $L\in\mathbb{R}$, then the sequence converges. If you doubt the outcome of your limit, then you could evaluate $a_n$ for large values of $n$ as a means to try to verify your result. Just be mindful that if $a_n$ contains a power of $-1$, then the sequence could oscillate between two limiting values and is thus divergent.

 

[chisigma]

what's the easiest way to quickly determine convergence or divergence? or is there a way to do it by calculator? i have a test today and most of the questions ill be given a series (few sequences) and itll be asking whether they converge or diverge?

What do you mean by 'easy' or 'quickly'? ... in Your place I would look for the most efficient test to determine if a series converges or diverges ... for the series with positive terms the more efficient test in my opinion is the Raabe test...

Kind regards

$\chi$ $\sigma$

 

[ineedhelpnow]

@chisigma i mean the simplest method that can help me get through the problems quickly