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Homework, Page 739

Homework, Page 739. Find the first six terms and the 100th term of the explicitly defined sequence. 1. . Homework, Page 739. Find the first four terms and the eighth term of the recursively defined sequence. 5. . Homework, Page 739.

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Homework, Page 739

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  1. Homework, Page 739 Find the first six terms and the 100th term of the explicitly defined sequence. 1.

  2. Homework, Page 739 Find the first four terms and the eighth term of the recursively defined sequence. 5.

  3. Homework, Page 739 Find the first four terms and the eighth term of the recursively defined sequence. 9.

  4. Homework, Page 739 Determine whether the sequence converges or diverges. If it converges, give the limit.. 13.

  5. Homework, Page 739 Determine whether the sequence converges or diverges. If it converges, give the limit.. 17.

  6. Homework, Page 739 The sequences are arithmetic. Find: (a) the common difference, (b) the tenth term, (c) a recursive rule for the nth term, and (d) an explicit rule for the nth term. 21.

  7. Homework, Page 739 The sequences are geometric. Find: (a) the common ratio, (b) the eighth term, (c) a recursive rule for the nth term, and (d) an explicit rule for the nth term. 25.

  8. Homework, Page 739 29. The fourth and seventh terms of an arithmetic sequence are – 8 and 4, respectively. Find the first term and a recursive rule for the nth term.

  9. Homework, Page 739 Graph the sequence. 33.

  10. Homework, Page 739 37. The bungy-bungy tree grows an average of 2.3 cm per week. Write a sequence that represents the height of a bungy-bungy over the course of one-year if it is 7 meters tall today. Display the first four terms and the last two terms.

  11. Homework, Page 739 43. If the first two terms of a geometric sequence are negative, then so is the third. Justify your answer. True, if the first two numbers are negative, then the common ratio must be positive and the multiplication of a negative number by a positive number yields another negative number.

  12. Homework, Page 739 45. The first two terms of an arithmetic sequence are 2 and 8. The fourth term is A. 20 B. 26 C. 64 D. 128 E. 256

  13. Homework, Page 739 47. A. 1 B. 4 C. 9 D. 12 E. 81

  14. 9.5 Series

  15. Quick Review

  16. Quick Review Solutions

  17. What you’ll learn about • Summation Notation • Sums of Arithmetic and Geometric Sequences • Infinite Series • Convergences of Geometric Series … and why Infinite series are at the heart of integral calculus.

  18. Summation Notation

  19. Sum of a Finite Arithmetic Sequence

  20. Example Summing the Terms of an Arithmetic Sequence

  21. Sum of a Finite Geometric Sequence

  22. Example Summing the Terms of a Finite Geometric Sequence

  23. Partial Sums Partial sums are the sums of a finite number of terms in an infinite sequence. In some instances, the partial sums approach a finite limit and the series is said to converge.

  24. Example Examining Partial Sums

  25. Infinite Series

  26. Sum of an Infinite Geometric Series

  27. Example Summing Infinite Geometric Series

  28. Homework • Homework Assignment #34 • Read Section 9.6 • Page 749, Exercises: 1 – 45 (EOO)

  29. 9.6 Mathematical Induction

  30. Quick Review

  31. Quick Review Solutions

  32. What you’ll learn about • The Tower of Hanoi Problem • Principle of Mathematical Induction • Induction and Deduction … and why The principle of mathematical induction is a valuable technique for proving combinatorial formulas.

  33. The Tower of Hanoi Solution The minimum number of moves required to move a stack of n washers in a Tower of Hanoi game is 2n – 1.

  34. Principle of Mathematical Induction Let Pn be a statement about the integer n. Then Pn is true for all positive integers n provided the following conditions are satisfied: • (the anchor) P1 is true; • (inductive step) if Pk is true, then Pk+1 is true.

  35. Example Proving a Statement Using Mathematical Induction Use mathematical induction to prove the statement holds for all positive integers.

  36. Induction and Deduction • Induction - the process of using evidence from a particular example to draw conclusions about general principles • Deduction - the process of using general principles to draw conclusions about specific examples

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