this week we learned more about convergence, divergence, p-series, nth term, integral test, and we learned something new called direct comparison test.
i'll be completely honest, and say that i am really confused with a lot of this stuff. idk why it just isn't sticking in my head.
i need someone to go over pretty much all of it... especially direct comparison test.
i also don't know the difference. whenever brob says what kind is this. idk how to tell if it's p-series, or something else. i'm really lost. idk, this just wasn't my best week.
i know they all have to do with sigmas. and i know what to do if the steps are in front of me. but idk, i guess i'm just lost.
sorry if this is a short post, i'm just in need of help mostly.
i'll go over at least one thing.
INFINITY RULES:
top degree > bottom degree = +/- infinity.
top degree < bottom degree = 0
top degree = bottom degree = divide coefficients
these are actually very helpful and never go away. a lot of the time we just automatically do l'hospitals rule whenever we could just be doing this!
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Okay. So when you're just given sigma something. and you want to see whether in converges or diverges, you have a multitude of things you can do. the first one you always do first the nth term. So basically you just, right off the bat, take the lim as n approaches inf. if this gives you zero, you have to move on to another method, but if you get anything besides zero, you can just say it diverges right away.
ReplyDeleteNow in the event that you get zero for the nth term, what you can do is just go down the list. check for geometric (number raised to some variable), p series (1 over n raised to some number) and integral test. If neither one of those works, your going to compare it to something smaller that way you can just say, well if the smaller one converges, then the original one will converge, and the opposite too.