Professor Kate Poirier | OL33 | Spring 2021

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

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

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.

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