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Calculus 2, part 2 of 2: Sequences and series
Single variable Calculus: sequences and series of numbers and of real-valued functions of one real variable
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- All Levels
- 60h 38m video
- 273 lectures
- English
- Captions
- Updated 2026
Taught by Hania Uscka-Wehlou
- 60h 38m of on-demand video
- 273 lectures across 16 sections
- One-off payment — no subscription
- Lifetime access on web and mobile
- Closed captions (English)
Curriculum
16 sections273 lectures60h 38m total
- Introduction to the course18:41
- Sequences in our earlier courses16:44
- Series in our earlier courses7:53
- Change of plans4:36
- Sequences and their convergence: a visual repetition32:06
- Why are sequences important to understand?7:36
- Arithmetic and geometric progressions, a repetition18:28
- Arithmetic and geometric sums, a repetition13:04
- Future, Optional: Continuous versus discrete26:40
- Old and new methods for determining convergence of sequences14:25
- Practicing rules of limits, Exercise 19:39
- Indeterminate forms and standard limits, Exercise 27:40
- Indeterminate forms and conjugates, Exercise 35:21
- Indeterminate forms and conjugates, Exercise 44:03
- Indeterminate forms and arithmetic on extended reals, Exercise 54:42
- Squeeze Theorem, Exercise 637:23
- Squeeze Theorem, Exercise 717:08
- An old promise from earlier courses6:05
- Indeterminate forms "one to the infinity", various situations11:10
- Indeterminate forms leading to a result with e, Exercise 89:01
- Indeterminate forms leading to a result with e, Exercise 910:39
- Indeterminate forms leading to a result with e, Exercise 106:36
- A difficult one, Problem 16:19
- A warm-up exercise, Exercise 127:25
- Proving (eventual) monotonicity analysing quotients, Exercise 229:52
- Proving (eventual) monotonicity analysing quotients, Exercise 312:34
- Proving (eventual) monotonicity, Exercise 412:53
- Proving (ev.) monotonicity by a little bit of Weierstrass cheating, Exercise 526:09
- Nested roots, Problem 118:03
- Recursively defined sequence, Problem 221:01
- Recursively defined sequence, Problem 313:32
- Recursively defined sequence, Problem 46:34
- Using Riemann integrals, Problem 520:16
- A version of Weierstrass' Theorem for unbounded monotone sequences11:03
- Coming closer to series, Problem 69:47
- Coming closer to series: telescoping series, Problem 715:59
- Coming closer to series: comparing stuff, Problem 87:23
- The one with a product, Problem 95:47
- Another one with a product, Problem 108:56
- The one tending to e, Problem 1112:07
- Monotonicity of geometric progressions using difference method20:16
- Using functions while working with sequences27:42
- Using functions while working with sequences, Exercise 122:22
- Using functions while working with sequences, Exercise 250:22
- Using functions while working with sequences, Exercise 318:15
- Using functions while working with sequences, Exercise 43:40
- Using functions while working with sequences, Exercise 53:37
- Using functions while working with sequences, Problem 119:05
- A spoiler: using functions while working with series17:02
- Stolz-Cesáro Theorem: formulation and proof19:52
- Applications of Stolz-Cesáro Theorem: Example 16:03
- Applications of Stolz-Cesáro Theorem: Example 2 (Cauchy's Theorem)18:06
- A corollary from Cauchy's Theorem10:44
- Applications of the corollary from V53, Example 37:07
- Applications of Stolz-Cesáro Theorem: Problem 119:16
- Using formulas or Riemann sums instead, Problem 215:05
- Geometric means, Problem 330:40
- Corollary from the fact proven in V576:33
- Applications of the corollary from V58, Example 47:53
- Ratio test for sequences5:57
- Ratio test for sequences, Problem 44:31
- Ratio test for sequences, Problem 56:02
- Ratio test for sequences, Problem 618:09
- Ratio test for sequences: Case 3 is inconclusive8:05
- Ratio test for sequences: the converse is not true17:20
- Verifying recurrence relations, Exercise 118:10
- Using iterations for getting the formula, Exercise 211:21
- Telescoping techniques, Exercise 37:58
- Linear recursion of order 2: an introduction, Exercise 420:25
- Linear recursion of order 2: the meaning of linearity, Exercise 529:55
- Linear recursion of order 2: derivation of the closed formula11:06
- Linear recursion of order 2, Exercise 69:12
- Linear recursion of order 2, with an initial condition, Exercise 714:53
- Linear recursion of order 2, with an initial condition, Exercise 819:02
- Back to Fibonacci, Exercise 98:58
About this course
Calculus 2, part 2 of 2: Sequences and series Single variable calculus [None of our courses are produced using AI; they are all real-human products.] S1. Introduction to the course You will learn: about the content of this course; you will also get a list of videos form our previous courses where the current topics (sequences and series) were discussed. S2. Number sequences: a continuation from Calc1p1 You will learn: more about sequences, after the introduction given in Calc1p1 (Section 5): in this …
Before you start
- Calculus 1: Limits and continuity (or equivalent)
- Calculus 1: Derivatives with applications (or equivalent)
- Calculus 2: Integrals with applications (or equilvalent)
- You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody's advantage if you ask your questions on the forum.
Who it’s for
- University and college students wanting to learn Single Variable Calculus (or Real Analysis)
- High school students curious about university mathematics; the course is intended for purchase and supervision by adults for these students
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