useful tip for speed on some mcqs: approaching infinity, n^c < c^n < n! (c is a constant not in [-1, 1] bc otherwise it'd be getting smaller approaching infinity).
I was sick during the day we covered this and could not figure out for the life of me how to do problems like 4 & 5. finally decided to look into it before the test and finally understand it better.
how come in problem 2 you negated the (-1)^n+1 for alternating series test when taking the limit but in problem 3 you added the (-1)^n when u took the limit? i thought you said you suppose to leave out the alternating part. maybe in problem 3 u arent using alternating test and im just mistaking it but then what test are u using if ur taking the limit of that entire alternating series?
In the last question which is 5 , isn’t it supposed to be ( conditionally converges ) at x=2 since the series diverges there ? Why did you choose x=0 although it converges there .
The series is absolutely convergent from (0,2) but that does not include the endpoints 0 and 2 because the limit in the ratio test converges when its less than 1 (not less than or equal to). The endpoints would technically be divergent. That's why when he plugs in 0 it is conditionally convergent and when he plugs in 2 it is fully divergent. Hope that made sense
useful tip for speed on some mcqs: approaching infinity, n^c < c^n < n! (c is a constant not in [-1, 1] bc otherwise it'd be getting smaller approaching infinity).
I was sick during the day we covered this and could not figure out for the life of me how to do problems like 4 & 5. finally decided to look into it before the test and finally understand it better.
Thank you for this helpful video, I'm wondering when you will upload the next lesseon video?
how come in problem 2 you negated the (-1)^n+1 for alternating series test when taking the limit but in problem 3 you added the (-1)^n when u took the limit? i thought you said you suppose to leave out the alternating part. maybe in problem 3 u arent using alternating test and im just mistaking it but then what test are u using if ur taking the limit of that entire alternating series?
In the last question which is 5 , isn’t it supposed to be ( conditionally converges ) at x=2 since the series diverges there ? Why did you choose x=0 although it converges there .
The series is absolutely convergent from (0,2) but that does not include the endpoints 0 and 2 because the limit in the ratio test converges when its less than 1 (not less than or equal to). The endpoints would technically be divergent. That's why when he plugs in 0 it is conditionally convergent and when he plugs in 2 it is fully divergent.
Hope that made sense
Algebros