Solutions for Series and Their Notations

Solutions to Try Its

1. 38

2. [latex]\text{26}\text{.4}[/latex]

3. [latex]\text{328}[/latex]

4. [latex]\text{-280}[/latex]

5. $2,025

6. [latex]\approx 2,000.00[/latex]

7. 9,840

8. $275,513.31

9. The sum is defined. It is geometric.

10. The sum of the infinite series is defined.

11. The sum of the infinite series is defined.

12. 3

13. The series is not geometric.

14. [latex]-\frac{3}{11}[/latex]

15. $92,408.18

Solutions to Odd-Numbered Exercises

1. An [latex]n\text{th}[/latex] partial sum is the sum of the first [latex]n[/latex] terms of a sequence.

3. A geometric series is the sum of the terms in a geometric sequence.

5. An annuity is a series of regular equal payments that earn a constant compounded interest.

7. [latex]\sum _{n=0}^{4}5n[/latex]

9. [latex]\sum _{k=1}^{5}4[/latex]

11. [latex]\sum _{k=1}^{20}8k+2[/latex]

13. [latex]{S}_{5}=\frac{5\left(\frac{3}{2}+\frac{7}{2}\right)}{2}[/latex]

15. [latex]{S}_{13}=\frac{13\left(3.2+5.6\right)}{2}[/latex]

17. [latex]\sum _{k=1}^{7}8\cdot {0.5}^{k - 1}[/latex]

19. [latex]{S}_{5}=\frac{9\left(1-{\left(\frac{1}{3}\right)}^{5}\right)}{1-\frac{1}{3}}=\frac{121}{9}\approx 13.44[/latex]

21. [latex]{S}_{11}=\frac{64\left(1-{0.2}^{11}\right)}{1 - 0.2}=\frac{781,249,984}{9,765,625}\approx 80[/latex]

23. The series is defined. [latex]S=\frac{2}{1 - 0.8}[/latex]

25. The series is defined. [latex]S=\frac{-1}{1-\left(-\frac{1}{2}\right)}[/latex]

27.
Graph of Javier's deposits where the x-axis is the months of the year and the y-axis is the sum of deposits.

29. Sample answer: The graph of [latex]{S}_{n}[/latex] seems to be approaching 1. This makes sense because [latex]\sum _{k=1}^{\infty }{\left(\frac{1}{2}\right)}^{k}[/latex] is a defined infinite geometric series with [latex]S=\frac{\frac{1}{2}}{1-\left(\frac{1}{2}\right)}=1[/latex].

31. 49

33. 254

35. [latex]{S}_{7}=\frac{147}{2}[/latex]

37. [latex]{S}_{11}=\frac{55}{2}[/latex]

39. [latex]{S}_{7}=5208.4[/latex]

41. [latex]{S}_{10}=-\frac{1023}{256}[/latex]

43. [latex]S=-\frac{4}{3}[/latex]

45. [latex]S=9.2[/latex]

47. $3,705.42

49. $695,823.97

51. [latex]{a}_{k}=30-k[/latex]

53. 9 terms

55. [latex]r=\frac{4}{5}[/latex]

57. $400 per month

59. 420 feet

61. 12 feet