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Never heard it called the absolute convergence test. Are you talking about the ratio test?

\[\lim_{n \rightarrow \infty} \left| a(n+1)/a(n) \right|\] ?

yes haha

But you can bypass that step by multiplying by the reciprocal once you get the hang of it.

yup got that, i'm having trouble simplifying that

Your k! when your replacing "k" with "k+1" will end up being "(k+1)!"

Is that what you meant or as you progress farther into the problem when you have k! over (k+1)!

further, taking the limit of the already established reciprocal

multiplaction step

ok. And what exact thing are you having trouble multiplying?

finding the limit

right now i have 1^(k+1)+1/(k+1)! * k!/1^(k+1)

so whats next? how do i find that limit/simplifiy that fraction

Let me look in my notes real quick

ok :)

cause i'll also need that rule to test the original function for convergence

The factorials cancel each other in a way.

..and you'll keep the constants right?

So the first term in what you have right now has a (k+1) in the denominator instead of (k+1)!

so i'll end up taking the limit of 1/k+1 ?

I believe so

wonderful :)

thanks for your help! :)

Your very welcome