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In the book there is an example that's \[\sum_{n=1}^{\infty} \frac{n}{(-2)^{n-1}}\]

Slight note: Monotonic over [1, infty]

how or why? the how is clear right? if \(n>1\) then \(\frac{n+1}{n}>\frac{1}{2}\) for sure

Well do you have to make a formal proof? Or an AP Calc BC-suitable proof?

Do we have to do stuff like this, or just apply the rules in the theorm to see if it wortks or not?

The course I'm in is Calc 2.

The book only says 2 conditons an+1 < an and an = 0.

Seems like a lot of L'hospitals rule is used.. Should bone up.

oh yeah it says let an > 0

LH is a good thing to always keep in your mind.

so hmm... can you check out the first picture and see what they are doing?

not sure if it's important for my needs.