Technical Mathematics, Sixth Edition

D.20. CHAPTER 20

Exercise 1

1. 3 + 6 + 9 + 12 + 15 + ... + 3n + ...

3. 2 + 3/4 + 4/9 + 5/16 + 6/25 + ... + (n + 1)/n² + ...

5. U_n = 2n; 8, 10

7. u_n = 2ⁿ/(n + 3); 32/8, 64/9

9. uⁿ = u_n−1 + 4; 13, 17

11. u_n = (u_n−1)²; 6561, 43,046,721

Exercise 2

1. 46

3. 43

5. 49

7. x + 24y

9.

11. 5, 11, 17, 23, 29, ...

13. −7

15. 234

17. 225

19. 15

21. 10, 15

23.

25. 3/14

29. 6/17, 6/13, 6/9

31. (a) $0.50, 1.00, 1.50, ... (b) $333

33. $512,500

Exercise 3

1. 80

3. −9375

5. 5115

7. −292,968

9. ±15

11. ±30

13. 24, 72

15. ±20, 80, ±320

17. e^1/2 or 1.649

19. 3.2°F

21. 8.3 yr

23. 28.8 ft

25. 62

27. 2.0

29. 1.97

31. $184,202

33. $7776

Exercise 4

1. 5 − c

3. 3/(c + 4)

5. 288

7. 12.5

9. 45.5 in.

11. sum = 1

Exercise 5

1. 720

3. 42

5. 35

21. 59, 136a¹²b¹⁸

23. −15, 120a⁴b³

25. 202, 400x²¹y²

Review Problems

1. 35

3. 6, 9, 12, 15

5.

7. 85

9. a⁵ − 10a⁴ + 40a³ − 80a² + 80a − 32

11. 48

13. 9 − x

15. 8

17. 5/7

19.

21. 1215

23. −1024

25. 20, 50

27. 1440

29. 252

31. 128x⁷/y¹⁴ − 448x^13/211 + 672x⁶/y⁸ − 560x^11/2/y⁵ + ...

33. 1 − a/2 + 3a²/5a³/16 + ...

35. −26,730a⁴b⁷