@narutokurosaki6477

my teacher soent an entire class period teaching this and I had no idea what he was even talking about. I see 5 minutes of this video, and I understood it completely. thanks so much

@Mathispower4u

Thank you for the comments!

@rodolfobarranco03

just a quick question, in minute 4 you compare the function 1/(n-2)^(1/2) to 1/n^(1/2) which is actually smaller than the original function. since the definition of the comparison test says that in order for this to work the function An has to be between 0 and Bn. in other words: 0<An<Bn, wouldn't the example you showed be wrong?

@alkajon

When writing out a factorial, you are multiplying by the starting number and every integer down to 1.  For example 3! = 3 * 2 * 1.  So if you have n!, as n increases, so does the factors that you are multiplying by, whereas the base of 2 you only ever multiply by 2 for any value of n-1.  3! > 2^2 because 6 > 4 and 4! > 2^3 because 24 > 8.  Essentially, the factorial increase faster than the exponent.

@shaheenhearts

you just took something that looks so horrible and scary on paper and turned it into something human friendly!! THANK YOUU SO MUCH!!! 

@SarkTheShark94

bullcleo1 > patrickJMT 
I find your videos more organized and clear. 
Thanks Man

@ethanlarue4881

@ 5:13 why are we saying is it >? and not <?

@3andhalfpac

you also could use 1/n^2 starting n at 4 since 4^2 is 16 and 4! is 24 as long as 1/n!> 1/n^2.  

@williamwarren9397

how do I know if its inconclusive?

@DADDY557

i think that is relating this n! to the"growth rates of sequences" which states that n! grows faster than b^n ....... that's how i think he got that random thing

@willytillyfilly

OMG THANK YOU FOR UPLOADING!!!!! You're a lifesaver. :D

@ac7491

That is an interesting cursor you have there.

@nycityzen

Why did you choose to compare n! to 2^n?

@sameergowani

we could also use the root test in the second example right?

@maithaap4565

thank you , such a life savor

@Mathispower4u

Yes, that is correct.  

@exile341

I don't understand example #2 Bn is smaller than An. The rule for the comparison test states that 0<an<=bn. what is missing here?

@ΔημήτρηςΠπαπαδόπουλος

great work !!! very helpful !!!

@muhammadkabir-ud-dinnawaz8706

Where can I get PDFs of these slides ?

@TheTechnicalPandyaji

what is the straterg to know which test to apply when