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Chapter 11: Problem 63

How do you determine how many terms there are in a binomial expansion?

Short Answer

Expert verified
If a binomial expression is raised to a power \(n\), the number of terms in the expanded form is \(n + 1\).

Step by step solution

01

Understand the Binomial Theorem

The binomial theorem states that the expansion of the power of a binomial has terms equal to the power's exponent increased by one. So if you have a binomial like \(a + b\) and you raise it to some power \(n\), the number of terms in the expanded form will be \(n + 1\).
02

Apply the rule to determine the number of terms

Using the rule from the binomial theorem noted above, you determine the number of terms by increasing the exponent of the binomial by one.

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Most popular questions from this chapter

Research and present a group report on state lotteries. Include answers to some or all of the following questions: Which states do not have lotteries? Why not? How much is spent per capita on lotteries? What are some of the lottery games? What is the probability of winning top prize in these games? What income groups spend the greatest amount of money on lotteries? If your state has a lottery, what does it do with the money it makes? Is the way the money is spent what was promised when the lottery first began?

Use the formula for the value of an annuity to solve Exercises 77鈥�84. Round answers to the nearest dollar. At age \(25,\) to save for retirement, you decide to deposit \(\$ 75\) at the end of each month in an IRA that pays \(6.5 \%\) compounded monthly. a. How much will you have from the IRA when you retire at age \(65 ?\) b. Find the interest.

A new factory in a small town has an annual payroll of S6 million. It is expected that \(60 \%\) of this money will be spent in the town by factory personnel. The people in the town who receive this money are expected to spend \(60 \%\) of what they receive in the town, and so on. What is the total of all this spending, called the total economic impact of the factory, on the town each year?

Use the formula for the value of an annuity to solve Exercises 77鈥�84. Round answers to the nearest dollar. To offer scholarship funds to children of employees, a company invests \(\$ 10,000\) at the end of every three months in an annuity that pays \(10.5 \%\) compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years? b. Find the interest.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I was able to find the sum of the first 50 terms of an arithmetic sequence even though I did not identify every term.
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