Well does it converge or diverge?
You should probably try the nth term test before trying another method.
P-Series: n^p
if p is greater than 1-->converge
if less than or eqaul to 1-->diverge
Geometric: (1/2)^n
if the absoultue value of r(which is the n) is less than 1-->converge
if the absoultue value of r greater than 1-->diverge
Intergral Test: Probably use when everything fails.
First, take the limit from 0 to infinity.
Second, integrate like normal.
Third, plug in 0 and infinity.
Finally, take the limit.
If you still get any form of infinity-->diverge
if you get a number-->converge.
Comparing: You can compare the problem to an eaiser one.
1. direct comparison
2. limit comparison
My Question: I need someone to explain the difference between direct and limit (the steps and everything). I'm afraid that I'm mixing them up or using a combination of both. Please help.
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Okay. For direct, you compare it to something BIGGER than the original. then use one of the normal steps (pseries, geo, etc.). If it converges, the original converges. And if it diverges, the original diverges.
ReplyDeletefor limit comparison, you can compare it to anything remotely similar. then you put the original over the new (I think) and take the limit as n goes to infinity.
Now, the only part I'M a little shady on is the whether or not the LCT diverges, what does that mean in terms of you original?