Direct comparison & limit comparison tests (8 examples) Calculus 2

Calculus 2 tutorial on the direct comparison test and the limit comparison test.
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Thanks to ‪@02_aldebaranrahmanadhitya95‬ for the timestamps!
0:00 8 examples for direct comparison or limit comparison test for series
Question 1: 0:01
Question 2: 4:31
Question 3: 6:23
Question 4: 8:33
Question 5: 13:01
Question 6: 15:59
Question 7: 19:31
Question 8: 21:50

[@02_aldebaranrahmanadhitya95]

Timestamps Question 1: 0:01 Question 2: 4:31 Question 3: 6:23 Question 4: 8:33 Question 5: 13:01 Question 6: 15:59 Question 7: 19:31 Question 8: 21:50

[@bprpcalculusbasics]

Thank you!!

[@tdchayes]

Since I tutor math, I appreciate that you consider what some teachers would like to see. "if your teacher ... divide everything by the largest power". It's important to be consistant with the classroom teaching.

[@skyethebi]

9:56 you can also split the sum into two parts one with numerator n and one with numerator 2 and you can show that by the DCT both converge and therefore their sum converges. Obviously it’s important to note that you can only split up this sum because both parts of the numerator are strictly positive for all n in the sum and therefore you wouldn’t have an infinity - infinity case.

[@izukanjisukwa8939]

7:16 it's suppose to be greater than or equal to 1/n

[@holyshit922]

Maybe some homework questions at the end of the video

[@bprpcalculusbasics]

Yes, 100 series! 😆

[@brennans1563]

Sweet

[@qpgaming9468]

thank you for this!! ❤ I keep hearing "dumber little part" instead of "dominating part"🤣

[@AyeAus]

19:30 was pretty cool 😂

[@cluelesshands9129]

♥

[@cyrusyeung8096]

From the limit comparison test, we know if a_n ∈ Θ(b_n), then both (sum of a_n) and (sum of b_n) converges / diverges. Similarly, can I say if a_n ∈ ω(b_n) and (sum of b_n) converges, then (sum of a_n) converges?