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Question : A ball is dropped from a height of 14 meters and returns to about 6/7 of its previous height on each bounce : 2163555

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

41) Determine the sum of the following geometric series: (2^{2}/5^{3}) + (2^{4}/5^{5}) + (2^{6}/5^{7}) + (2^{8}/5^{9}) + (2^{10}/5^{11}) + ... .

Enter just a reduced fraction of form (a/b).

42) Determine the sum of the following geometric series: 1 + (1/√(2)) + (1/2) + ... .

Enter your answer exactly in the form (√(a)/√(a) - b).

43) Determine the sum of the following geometric series: 2 + (4/3) + (8/9) + ... .

Enter just an integer.

44) Determine the sum of the following geometric series: 3 - 1.8 + 1.08 + .648 - ... .

Enter just a real number rounded off to three decimal places.

45) Determine the sum of the following geometric series: (27/5) + (18/5) + (12/5) + (8/5) + ... .

Enter a reduced fraction of form (a/b).

46) Determine the sum of the following geometric series: 1 + (0.25)^{2} + (0.25)^{4} + (0.25)^{8} + ... .

Enter a reduced fraction of form (a/b).

47) Sum an appropriate infinite series to find the rational number whose decimal expansion is: .

Enter just a reduced fraction of form (a/b).

48) Sum an appropriate infinite series to find the rational number whose decimal expansion is: .

Enter just a reduced fraction of form (a/b).

49) Sum an appropriate infinite series to find the rational number whose decimal expansion is: . Enter just a reduced fraction of form (a/b).

50) Sum an appropriate infinite series to find the rational number whose decimal expansion is: .

Enter just a reduced fraction of form (a/b).

51) Determine the sum of the following infinite series: .

Enter just an integer.

52) Determine the sum of the following infinite series: .

Enter just a reduced fraction of form (a/b).

53) Determine the sum of the following infinite series: .

Enter your answer exactly in the reduced form (a/√(b)).

54) Determine the sum of the following infinite series: .

Enter just an integer.

55) Determine the sum of the following infinite series: Enter just a reduced fraction of form (a/b).

56) Determine the sum of the infinite geometric series

Enter your answer exactly in the reduced form (a lnb/c).

57) Determine the sum of the following series: 10 + 4 + (8/5) + (16/25) + ... .

Enter just a reduced fraction of form (a/b).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

58) Determine the sum of the geometric series (2^{2}/5^{2}) - (2^{3}/5^{3}) + (2^{4}/5^{4}) - ..., if it is convergent.

A) (5/7)

B) (7/5)

C) (3/5)

D) (4/35)

E) none of these

59) Determine the sum of the infinite series:

A) 2

B) (4/3)

C) (2/3)

D) (4/5)

E) none of these

60) The geometric series 1 + (0.2)^{3} + (0.2)^{6} + (0.2)^{9} + ...

(I) converges

(II) is equal to

(III) is equal to

A) I and III

B) II and III

C) I, II, and III

D) III only

E) I and II

Solve the problem.

61) The infinite series a_{1} + a_{2} + a_{3} + ... has partial sums given by S_{n} = 1 - (3/n). Find

A) 1.3

B) 7

C) 0.7

D) 0.97

62) The infinite series a_{1} + a_{2} + a_{3} + ... has partial sums given by S_{n} = 8 - (3/n). Does the infinite series converge? If so, to what value does it converge?

A) Yes, 8

B) Yes, 11

C) Yes, 5

D) No, (8 - (3/n)) does not exist

63) England decides to decrease its taxes by £7 billion. It is estimated that of each pound received, a typical citizen will spend 90%. The level of economic activity generated by the tax cut is therefore estimated to be: 7?(0.90) + 7?(0.90)^{2} + 7?(0.90)^{3} + ... billion pounds. This amount is equal to what?

A) £3.6 billion

B) £45 billion

C) £63 billion

D) £70 billion

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

64) A student receives $1000 at the start of each month from his parents. Every month the student spends 70% of all the money he has. If the only money the student receives is the money from his parents, estimate how much money the student will have at the beginning of each month after an extended period of time.

Enter just a reduced fraction of form (a/b).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

65) A patient receives M milligrams of a certain drug every hour. Each hour the body eliminates a fraction p of the amount of drug in the body. After an extended period of time, which of the following series approximates the amount of drugs present in the patient's body immediately before receiving an hourly dose?

A)

B)

C)

D)

E)

66) Consider the following geometric series: (25/2) - (15/2) + (9/2) - (27/10) + ... . Which of the following statements is true?

A) The ratio r of this series is (3/5).

B) The sum of this series is (125/4).

C) This series diverges.

D) Another way writing this series is

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

67) Suppose converges. What can you say about the value of m?

Enter your answer in standard interval notation (no variables).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

68) A ball is dropped from a height of 14 meters and returns to about 6/7 of its previous height on each bounce. About how far will the ball travel before it comes to rest?

A) 266 m

B) 98 m

C) 182 m

D) 350 m

69) A pendulum bob swings through an arc 40 centimeters long on its first swing. For each swing thereafter, it swings only 95% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?

A) (475/7) cm

B) (800/39) cm

C) 800 cm

D) (475/3) cm

70) After being struck with a hammer, a gong vibrates 30 vibrations in the first second and in each second thereafter makes (3/4) as many vibrations as in the previous second. Find how many vibrations the gong makes before it stops vibrating.

A) 40 vibrations

B) 120 vibrations

C) 35 vibrations

D) 130 vibrations