Professor Kate Poirier | OL33 | Spring 2021

Category: Week 12 group post (Page 1 of 4)

Group #3 Week 12 mega group

Vickram – Taylor Polynomials ( Question #1 – Test #2 )

Omesh Persaud- Divergence test (Question #1- Test #2)

Cristofer Martinez – Conditional Convergence (Question #1 – Test #2)

Daron Roye (Partial Sums – Question: 7, Test:#2)

Group #1 was not there in the meeting and did not reach to us so we are publishing the work that our group has worked on our group meeting

Test #2 Cheat sheet

Brygetee

Eduardo 

Aleem 

Zenab

  1. Lesson 11 Taylor and Maclaurin Polynomials (part 1)

Rederely: Series Taylor and Maclaurin Polynomials Question 1

3. Lesson 13 Sequences

Rederly: Series_Sequences Question 1

4. Lesson 14 Infinite Series

Rederly: series_infinite series Question 1 

5. Lesson 15  Integral and Divergence Tests

Hot Topic Standard #8

     6. Standard 8 Integral and Divergence tests

                   Ratio Test

L

         7. Lesson 19 Power series

         Rederly  power_series question 9

8. Hot topic standard 7

Determine whether a series converges absolutely, conditionally, or diverges.

Hot Topic Standard 9

Find radius and interval of convergence of a power series.

Test #2 Individual Cheat Sheet

11-12. Taylor and Maclaurin Polynomials

13. Sequences

Arithmetic Sequence:

Geometric Sequence:

Convergence of Sequence:


14. Infinite Series

Infinite Sequence:

If a sequence is a list of numbers: … then a series is just the sum of the terms in the series: …

Infinite Series:

Geometric Series:

Partial Sum of Geometric Series:

Converging and Diverging Series:

For the infinite series

the nth partial sum is given by

If the sequence of partial sums converges to L, then the series converges where L is the sum of the series.

If diverges, then the series diverges.

Divergent Test for a Series:

 

Telescoping Infinite Series:

The telescoping series is of the form

The series will only converge if and only if approaches a finite number as n approaches infinity.

15. The Divergence and Integral Tests:

Integral Test:

  • The interval does not always need to start at 1.
  • The function does not necessarily always need to be decreasing. It needs to decrease for the x-value larger than 1.

P-Series Test:

Divergence Test:

16. Comparison Tests:

Comparison Test:

Limit Comparison Test:

17. Alternating Series Test:

Alternating Series Test:

The alternating series test applies to the alternating harmonic series because the individual terms satisfy the three conditions:

So the alternating harmonic series   converges by the alternating series test.

Absolute and Conditional Convergence:

This means that there are three possibilities for any given series: the series either converges absolutely or conditionally, or the series diverges.

18. Ratio and Root Test:

Ratio Test:

Root Test:

19. Power Series and Functions & Properties of Power Series:

Power Series:

Interval of Convergence:

20. Taylor and Maclaurin Series & Working with Taylor Series:

Taylor Series

 

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