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Study Guides > Precalculus II

Solutions for Series and Their Notations

Solutions to Try Its

1. 38 2. 26.4\text{26}\text{.4} 3. 328\text{328} 4. -280\text{-280} 5. $2,025 6. ≈2,000.00\approx 2,000.00 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. −311-\frac{3}{11} 15. $92,408.18

Solutions to Odd-Numbered Exercises

1. An nthn\text{th} partial sum is the sum of the first nn 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. ∑n=045n\sum _{n=0}^{4}5n 9. ∑k=154\sum _{k=1}^{5}4 11. ∑k=1208k+2\sum _{k=1}^{20}8k+2 13. S5=5(32+72)2{S}_{5}=\frac{5\left(\frac{3}{2}+\frac{7}{2}\right)}{2} 15. S13=13(3.2+5.6)2{S}_{13}=\frac{13\left(3.2+5.6\right)}{2} 17. ∑k=178⋅0.5k−1\sum _{k=1}^{7}8\cdot {0.5}^{k - 1} 19. S5=9(1−(13)5)1−13=1219≈13.44{S}_{5}=\frac{9\left(1-{\left(\frac{1}{3}\right)}^{5}\right)}{1-\frac{1}{3}}=\frac{121}{9}\approx 13.44 21. S11=64(1−0.211)1−0.2=781,249,9849,765,625≈80{S}_{11}=\frac{64\left(1-{0.2}^{11}\right)}{1 - 0.2}=\frac{781,249,984}{9,765,625}\approx 80 23. The series is defined. S=21−0.8S=\frac{2}{1 - 0.8} 25. The series is defined. S=−11−(−12)S=\frac{-1}{1-\left(-\frac{1}{2}\right)} 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 Sn{S}_{n} seems to be approaching 1. This makes sense because ∑k=1∞(12)k\sum _{k=1}^{\infty }{\left(\frac{1}{2}\right)}^{k} is a defined infinite geometric series with S=121−(12)=1S=\frac{\frac{1}{2}}{1-\left(\frac{1}{2}\right)}=1. 31. 49 33. 254 35. S7=1472{S}_{7}=\frac{147}{2} 37. S11=552{S}_{11}=\frac{55}{2} 39. S7=5208.4{S}_{7}=5208.4 41. S10=−1023256{S}_{10}=-\frac{1023}{256} 43. S=−43S=-\frac{4}{3} 45. S=9.2S=9.2 47. $3,705.42 49. $695,823.97 51. ak=30−k{a}_{k}=30-k 53. 9 terms 55. r=45r=\frac{4}{5} 57. $400 per month 59. 420 feet 61. 12 feet

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