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- Binomial theorem
Key equations
Binomial Theorem |
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term of a binomial expansion |
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Key concepts
-
is called a binomial coefficient and is equal to
See
[link] .
- The Binomial Theorem allows us to expand binomials without multiplying. See
[link] .
- We can find a given term of a binomial expansion without fully expanding the binomial. See
[link] .
Section exercises
Verbal
What is a binomial coefficient, and how it is calculated?
A binomial coefficient is an alternative way of denoting the combination
It is defined as
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What is the Binomial Theorem and what is its use?
The Binomial Theorem is defined as
and can be used to expand any binomial.
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Algebraic
For the following exercises, evaluate the binomial coefficient.
For the following exercises, use the Binomial Theorem to expand each binomial.
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.
Graphical
For the following exercises, use the Binomial Theorem to expand the binomial
Then find and graph each indicated sum on one set of axes.
Extensions
In the expansion of
each term has the form
successively takes on the value
If
what is the corresponding term?
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Find
and write the answer as a binomial coefficient in the form
Prove it.
Hint: Use the fact that, for any integer
such that
Proof:
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Which expression cannot be expanded using the Binomial Theorem? Explain.
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The expression
cannot be expanded using the Binomial Theorem because it cannot be rewritten as a binomial.
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Questions & Answers
what does mean opportunity cost?
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economics theory describes individual behavior as the result of a process of optimization under constraints the objective to be reached being determined by
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Economics is a branch of social science that deal with How to wise use of resource ,s
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Economic Needs: In economics, needs are goods or services that are necessary for maintaining a certain standard of living. This includes things like healthcare, education, and transportation.
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Money market is a branch or segment of financial market where short-term debt instruments are traded upon. The instruments in this market includes Treasury bills, Bonds, Commercial Papers, Call money among other.
Examine the distinction between theory of comparative cost Advantage and theory of factor proportion
a general and ongoing rise in the level of prices in an economy
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What are the factors that affect demand for a commodity
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
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how is the graph works?I don't fully understand
hi guys good evening to all
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In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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