Thank you for the comments!
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?
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.
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@ 5:13 why are we saying is it >? and not <?
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.
how do I know if its inconclusive?
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
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That is an interesting cursor you have there.
Why did you choose to compare n! to 2^n?
we could also use the root test in the second example right?
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Yes, that is correct.
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?
great work !!! very helpful !!!
Where can I get PDFs of these slides ?
what is the straterg to know which test to apply when
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