No, this renders the use of the AST ineffective because often criterion number 1 is not met. In that case, you will need to resort to other convergence or divergence tests (like the "divergence test" that bprp used for q2). Greetings from Chile!
Wouldn't the harmonic series pass both those tests and be deemed to be convergent? Is it a requirment that the terms are alternating? Probably, but how come, is it by definition? Something I am not getting here. Happy to get an explanation :)
Yes, the series must be alternating. This is because an alternating series essentially “bounces” over and under its result, but getting closer each time. The harmonic series doesn’t converge because, while each fraction seems to be getting smaller, it still adds to the total. If it were (-1)^n/n, I believe it would converge by the AST.
![[[我有M1/M2數要問]] HKDSE M2 Q20250126|| Integration|| t-formula|| HKDSE M2](http://i.ytimg.com/vi/jdNOiGCkIlw/mqdefault.jpg)
Timestanps
Question 1: 0:01
Question 2: 3:47
Question 3: 6:22
Question 4: 10:40
Thank you so much!
Thank you for videos lately. Sequences and series were a struggle for me. Idk why 😅😅😅. The memories!
🔥these vids are gonna make me an academic weapon
Thank you!
For q2, can we say that it diverges since limit of b_n = (n + 1)/(3n + 2) as n approaches infinity ≠ 0 by Alternating Series Test?
No, this renders the use of the AST ineffective because often criterion number 1 is not met. In that case, you will need to resort to other convergence or divergence tests (like the "divergence test" that bprp used for q2).
Greetings from Chile!
Wouldn't the harmonic series pass both those tests and be deemed to be convergent? Is it a requirment that the terms are alternating? Probably, but how come, is it by definition? Something I am not getting here. Happy to get an explanation :)
Yes, the series must be alternating. This is because an alternating series essentially “bounces” over and under its result, but getting closer each time. The harmonic series doesn’t converge because, while each fraction seems to be getting smaller, it still adds to the total. If it were (-1)^n/n, I believe it would converge by the AST.
Sir, why did you not solve the question 2 by AST?
I just noticed bros huge red and blue markers stack
cant we say that question no 2 diverges since it fails AST as lim as n -> infinity is 1/3 which is not 0?
sir, i have a calculus problem, can you please help me to solve this question? And How do I send the question to you?