Infinite Geometric Series Assignment

Which expression accurately represents the infinite sum?

(A) 0.23/(1-0.01)

Which of the following geometric series is a representation of the repeating decimal 0.999999...?

(A) 0.99 + 0.0099 + 0.000099 + ... and (C) 0.9 + 0.09 + 0.009 + ...

Find the following partial sums: S2 = _____ S3 = _____

(A) 3/20, (B) 91/600

Find the sum of the infinite geometric series: [imagine the image here]

(B) 1,364

What is the simplest form of the fraction that represents this repeating decimal?

(B) 23/99

Which shows the exact distance traveled during the first six swings?

(B) 30(1-0.9^6/1-0.9)

About how far does the pendulum swing before coming to rest?

(B) 300 inches

Evaluate the infinite geometric series.

(B) 5/33

The series converges to a value that is _______ the initial term.

(B) less than

Torrey starts a new job with an annual salary of $60,000. For each year she continues to work for the same company, she will receive a 3 percent raise.If Torrey stays at this job, which shows how much she will have made over the course of her career?

(C) 60,000 + 61,800 + 63,654 + ...

Does the sum of the infinite series converge?

(C) Yes, because |r| < 1.

Find the sum of the infinite geometric series: 9.8+(-7.84)+6.272...

(D) 5 4/9

Repeated decimals can be written as an infinite geometric series to help convert them to a fraction. Consider the repeating decimal below.0.232323... = 0.23 + 0.23(0.01) + 0.23(0.01)2 + ... What is a1? What is r?

0.23, 0.01

Answer the following questions using the series representation. 0.9 + 0.09 + 0.009 + ... The first term is, _____ and the common ratio is _____.

0.9, 0.1

The repeating decimal 0.99999... converges to _____.

1

Find the areas of these shaded triangles. Orange: 1/4 square units Blue: _____ square units Green: _____ square units If the pattern continues indefinitely, does the sum of the areas converge?

1/16, 1/64, yes

If the pattern continues indefinitely, the sum of the areas is _____ square units.

1/3

Consider the infinite geometric series: What is a1? What is r?

1/6, -1/10

A pendulum travels 30 inches on its first swing. During each of its subsequent swings, it travels 90 percent of the previous swing. What is a1? What is r?

30, 0.9

When will an infinite geometric series with -1 < r < 0 converge to a number less than the initial term? Explain your reasoning, and give an example to support your answer.

If r is negative, the denominator of the formula for the sum of the series is positive and greater than 1. If the initial term is divided by a positive number greater than 1, the result is a number smaller than the initial term. So, if the initial term is positive, then the series will converge to a number less than the initial term. For -1 < r < 0, an example with a1 > 0, such as 1,000 - 100 + 10 - 1 + ...

Does the infinite sum converge or diverge?

diverge