Calculus 2 Series Convergence Test Review (alternating series test, ratio test, and root test)

Infinite series convergence tests! In this video, we will go over the alternating series test, ratio test, and root test. We will also talk about the meaning of conditional convergence and absolute convergence.
Get the file and the notes first: / 102348401
0:00 review on AST, ratio test, root test
7:15 Q1 series of (-1)^(n-1)*n/2^n
11:42 Q2 series of n/2^n
16:27 Q3 series of sin(n)/(n^2+1)
22:44 Q4 series of 1/(ln(n))^n
25:58 Q5 alternating series
29:03 Q6 series of (1-1/n)^n
33:46 Q7 series of n!/e^(n^2)
37:26 Q8 series of (2n)!/n^n
**series of n/2^n • Series of n/2^n **
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[@opufy]

Thank god for you. Would be nice to have a part 4: Power series, Taylor Series, Maclaurin series.

[@bprpcalculusbasics]

I got you here “power series ultimate study guide”
th-cam.com/video/LKhvdkUdLtE/w-d-xo.html

[@darkkevindu6982]

25:40 "as n goes from 1 to infinity" 1/ln(1) diverges + convergent limit = divergent limit, the conclusion is comically false due to careless error x)

[@KomalPatel-my8ws]

#Classify the series as absolutely convergent or conditionally convergent or divergent..
(a) 1-(1/1!)+(1/2!)-(1/3!)+....
(b)1-(1/3)+(1/5)-(1/7)+....
(c)(1/2)-(2/3)+(3/4)-(4/5)+....
(d)1-1+(1/2)-(1/2)+(1/3)-(1/3)+....
(e)1-(1/2)+(1/2)-(1/2²)+(1/3)-(1/2³)+(1/4)-(1/2⁴)+.....
Sir... please reply this..!!!!🙏🙏🙏

[@KomalPatel-my8ws]

Series 1-1+(1÷2)-(1÷2)+(1÷3)-(1÷3)+...... is absolutely convergent or conditionally convergent or divergent..??

[@AnakinSkywalker-zq6lm]

How can I email you and asks you a VERY important question

[@reidpattis3127]

26:40. There are some genuine merits of preferring the traditional lim notation rather than writing out “as n approaches infinity “.
My case:
1. There is NO confusion as to whether you’re reasoning with limits rather than arithmetic expressions. And it gives you clarity. I’ve had textbooks where the author felt lazy and just wrote at the beginning of a long proof, “as n approaches infinity “. It was a NIGHTMARE to understand and follow along with the proof. I Had to rewrite it in traditional lim notation to understand it. The more complicated and the mathematical jargon is, the more you need to rely on solid math notation to convey your message. Or heck if the math you’re doing is complex enough, to keep your own sanity you need to use proper notations.
2. It’s mathematically rigorous. What does it MEAN to let N approach infinity? Yes. We have a rough sense of that. But what is it concretely? It means to take a limit. Hence lim notation seems very appropriate.
Now I’m not saying that n approaching infinity can never be used. But I think when you’re starting out, be disciplined. When using limits has become second nature to you, then use the “as n approaches infinity” phrase in cases where it’s difficult to get confused.

[@Anionic_Official]

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