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After reading a few topics on this forum, i just realized that i had misunderstood the sequence v/s series theorem when it concerns the alternating sign. So, i went back to my notes, and i'm surprised to see that there is no mention of a series test. There is only a sequence test for alternating sign where i need to take the modulus. I guess my tutor skipped that part, or i lost my sheets. Either way, i'm now trying to learn the concept by myself.

The attempt at a solution

Here is what i've understood:

The AST is used to test for a series' convergence.

The first step is to check if: [tex]\lim_{n\rightarrow \infty} a_n = 0[/tex]

The second check is if: [tex]a_{n+1} \leq a_n[/tex]

I got those equations online (youtube), so i hope these are correct. However, i have several doubts:

What if the first check is OK but the second check is not. Does that mean that the series diverges?

In the example that i've seen in some video, i see that if the first check fails, then it automatically diverges. But i'm wondering if that's always the case?

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# Homework Help: Question about Alternating Series Test

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