I am trying to do an alternating series test problem but i forgot how to prove if the series is decreasing. I remember they were several tests for that, but i forgot which where. Please help!

Question

freckles · Answer

Can you show me your series?

freckles · Answer

Sometimes it is pretty easy with derivative. Sometimes it is easy with algebra. like we can show $$a_{n+1}<a_n \text{ for }n \text{ using algebra } \ \text{ or show } f' \text{ is negative for all } x$$

freckles · Answer

n not x

blackstreet23 · Answer

could you tell me all the tests? I am trying to review my calc 2 to be ready for calc 3

freckles · Answer

Those are the only two I can recall.

solomonzelman · Answer

In alternating series, if the absolute value of the terms decreases then the series will converge.

blackstreet23 · Answer

attachment

solomonzelman · Answer

So, I will denote the sums with $\rm S_1,~S_2...$
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