Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Chapter 5, Problem 46E
To determine
The value of
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Solve the rational equation
14
1
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x-7
○
a) x = 1, x = 8
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○ d) x = 1, x = 7
Solve the absolute inequality
| x + 5 > 3
○ a) (-∞, -8] U[-2, ∞0)
☐ b) (-8, -2)
c) (-2, ∞0)
○ d) (-∞, - 8) U(-2, ∞0)
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Describe the error in the problem
X 3
X
x
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2
=
25x = 0
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x = ±5
Chapter 5 Solutions
Introductory Combinatorics
Ch. 5 - Prob. 1ECh. 5 - Fill in the rows of Pascal’s triangle...Ch. 5 - Consider the sum of the binomial coefficients...Ch. 5 - Expand (x + y)5 and (x + y)6 using the binomial...Ch. 5 - Expand (2x − y)7 using the binomial theorem.
Ch. 5 - What is the coefficient of x5y13 in the expansion...Ch. 5 - Use the binomial theorem to prove that
Generalize...Ch. 5 - Use the binomial theorem to prove that
Ch. 5 - Evaluate the sum
Ch. 5 - Use combinatorial reasoning to prove the identity...
Ch. 5 - Use combinatorial reasoning to prove the identity...Ch. 5 - Let n be a positive integer. Prove that
(Hint:...Ch. 5 - Find one binomial coefficient equal to the...Ch. 5 - Prob. 14ECh. 5 - Prove, that for every integer n > 1,
Ch. 5 - By integrating the binomial expansion, prove that,...Ch. 5 - Prob. 17ECh. 5 - Evaluate the sum
Ch. 5 - Sum the series by observing that
and using the...Ch. 5 - Find integers a, b, and c such that
for all m....Ch. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Use a combinatorial argument to prove the...Ch. 5 - Let n and k be integers with 1 ≤ k ≤ n. Prove...Ch. 5 - Let n and k be positive integers. Give a...Ch. 5 - Let n and k be positive integers. Give a...Ch. 5 - Find and prove a formula for
where the summation...Ch. 5 - Prove that the only antichain of S = {1, 2, 3, 4}...Ch. 5 - Prove that there are only two antichains of S =...Ch. 5 - Let S be a set of n elements. Prove that, if n is...Ch. 5 - Construct a partition of the subsets of {1, 2, 3,...Ch. 5 - In a partition of the subsets of {1,2, …, n} into...Ch. 5 - A talk show host has just bought 10 new jokes....Ch. 5 - Prove the identity of Exercise 25 using the...Ch. 5 - Use the multinomial theorem to show that, for...Ch. 5 - Use the multinomial theorem to expand (x1 + x2 +...Ch. 5 - Determine the coefficient of in the expansion...Ch. 5 - What is the coefficient of in the expansion of
Ch. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Prove by induction on n that, for n a positive...Ch. 5 - Prove that
where the summation extends over all...Ch. 5 - Prove that
where the summation extends over all...Ch. 5 - Use Newton’s binomial theorem to approximate .
Ch. 5 - Use Newton’s binomial theorem to approximate...Ch. 5 - Use Theorem 5.6.1 to show that, if m and n are...Ch. 5 - Use Theorem 5.6.1 to show that, if m and n are...Ch. 5 - Prob. 50ECh. 5 - Let R and S be two partial orders on the same set...
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