1. Section 8.1: Sequences Practice HW from Stewart Textbook (not to hand in) p. 565 # 3-33 odd

2. Sequences Sequences are collection of numbers or objects that is ordered by the positive integers. Notation: (known as the terms of the sequence).

3. Example 1: Write the first five terms of the sequence. Solution:

5. Example 2: Write the first five terms of the sequence. Solution:

7. Describing the nth term of a sequence Involves writing a formula describing the pattern the sequence of numbers follows.

8. Example 3: Find a formula for the general term of the sequence. Solution:

9. Example 4: Find a formula for the general term of the sequence. Solution:

10. Convergence of Sequences Sequences whose behavior approaches a limiting value are said to converge to this value

11. Example 5: What value does the sequence appear to converge to? Solution:

12. Definition A sequence has the limit L and we write which is read approaches L as n approaches if we can make the terms as close to L as we like by taking n sufficiently large. If exists, then the sequence is convergent. Otherwise, it is divergent.

13. Useful Facts for Showing Convergence of Sequences 1. L Hopital’s Rule for indeterminate forms. 2. Absolute Value Theorem: If, then. 3. Using Maple to graph.

14. Example 6: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution:

15. Example 7: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution:

16. Example 8: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution:

18. Example 9: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution:

19. Example 10: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution: (In typewritten notes)

20. Example 11: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution:

22. Factorial Recall that, read as n factorial, is defined to be Note:.

23. Example 12: Compute. Solution:

24. Example 13: Determine whether the sequence converges or diverges. If the sequence converges, find the limit. Solution: (In typewritten notes)