Question 1

If  , use mathematical induction to show that  for all positive integers n .

Accepted Answer

The answer of If  , use mathematical induction to...

Question 2

Use the Binomial Theorem to expand and simplify the expression.

Accepted Answer

The answer of Use the Binomial Theorem to expand and...

Question 3

Find the sixth term without expanding.

Accepted Answer

The answer of Find the sixth term without expanding. 
...

Question 4

Use the Binomial Theorem to simplify the power of the complex number.

Accepted Answer

The answer of Use the Binomial Theorem to simplify the...

Question 5

Use the Binomial Theorem to expand and simplify the expression.

Accepted Answer

The answer of Use the Binomial Theorem to expand and...

Question 6

Use mathematical induction to prove the formula for every positive integer n . Show all your work.

Accepted Answer

The answer of Use mathematical induction to prove the formula...

Question 7

Find the sum of the infinite geometric series.

Accepted Answer

The answer of Find the sum of the infinite geometric...

Question 8

To save for the replacement of a computer, a business deposits $300 at the end of each month into an account that earns 5% annual interest compounded monthly. Find the future value of the ordinary annuity in 4 years.

Accepted Answer

The answer of To save for the replacement of a...

Question 9

Find the sum of the infinite geometric series.

Accepted Answer

The answer of Find the sum of the infinite geometric...

Question 10

Find the sum of the finite geometric series. Round to the nearest hundredth.

Accepted Answer

The answer of Find the sum of the finite geometric...

Question 11

Suppose that $500,000 of counterfeit money is currently in circulation and that each time the counterfeit money is used, 35% of it is detected and removed from circulation. How much counterfeit money, to the nearest thousand dollars, is used in transactions before all of it is removed from circulation?

Accepted Answer

The answer of Suppose that $500,000 of counterfeit money is...

Question 12

Find the sum of the finite geometric series.

Accepted Answer

The answer of Find the sum of the finite geometric...

Question 13

Find the fifth term without expanding.

Accepted Answer

The answer of Find the fifth term without expanding. 
...

Question 14

Prove the inequality for the indicated integer values of n .

Accepted Answer

The answer of Prove the inequality for the indicated integer...

Question 15

Find the indicated n th term of the geometric sequence. 4th term:

Accepted Answer

The answer of Find the indicated n th term of...

Question 16

Write the rational number  as the quotient of two integers in simplest form.

Accepted Answer

The answer of Write the rational number  as the...

Question 17

A letter listing the names and addresses of 8 people was sent to 3 other people, who were asked to send $5 to the name at the top of the list and then remove that person's name. Each recipient then added his or her name to the bottom of the list and sent the letter to five friends. Assuming no one broke the chain, how much money would each recipient of the letter receive?

Accepted Answer

The answer of A letter listing the names and addresses...

Question 18

Find the sum of the infinite geometric series below.

Accepted Answer

The answer of Find the sum of the infinite geometric...

Question 19

Sometimes a city will argue that having a professional sports franchise in the city will contribute to economic growth. The rationale for this statement is based on the multiplier effect. Suppose a city estimates that a professional sports franchise will create $45 million of additional income and that a person receiving a portion of this money will spend 80% and save 20%. Assuming the multiplier effect model is accurate, what is the net effect of the $45 million? Round to the nearest hundred thousand.

Accepted Answer

The answer of Sometimes a city will argue that having...

Question 20

Find the n th term of the geometric sequence.

Accepted Answer

Unfortunately, since we do not have access to the actual sequence, we cannot determine the correct answer. The given sequence of letters and numbers does not provide enough information to find the common ratio or first term of the sequence. Thus, the answer is purely a matter of guessing.

Quiz 11: Sequences, Series, and Probability

If , use mathematical induction to show that for all positive integers n .

Use the Binomial Theorem to expand and simplify the expression.

Find the sixth term without expanding.

Use the Binomial Theorem to simplify the power of the complex number.

Use the Binomial Theorem to expand and simplify the expression.

Use mathematical induction to prove the formula for every positive integer n . Show all your work.

Find the sum of the infinite geometric series.

To save for the replacement of a computer, a business deposits $300 at the end of each month into an account that earns 5% annual interest compounded monthly. Find the future value of the ordinary annuity in 4 years.

Find the sum of the infinite geometric series.

Find the sum of the finite geometric series. Round to the nearest hundredth.

Find the sum of the finite geometric series.

Find the fifth term without expanding.

Prove the inequality for the indicated integer values of n .

Find the indicated n th term of the geometric sequence. 4th term:

Write the rational number as the quotient of two integers in simplest form.

Find the sum of the infinite geometric series below.

Find the n th term of the geometric sequence.