Explanation Formula used: For positive integer n and r , C ( n , r ) = n ! r ! ( n − r ) ! . Calculation: Simplify both sides of the equation separately. L H S = 2 C ( n , 2 ) + n 2 = 2 n ! 2 ! ( n − 2 ) ! + n 2 = 2 n ⋅ ( n − 1 ) ⋅ ( n − 2 ) ! 1 ⋅ 2 ⋅ ( n − 2 ) ! + n 2 = 2 n 2 − n Similarly, simplify the right hand side as follows

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ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 8.1, Problem 30E

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To prove: The equation 2C(n,2)+n2=C(2n,2) for n≥2.

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Chapter 8.1, Problem 29E

Chapter 8.2, Problem 1E

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Chapter 8 Solutions

Discrete Mathematics

Ch. 8.1 - Evaluate the numbers in Exercises 1-12. C(5, 3) Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. C(12, 7) Ch. 8.1 - Prob. 5E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Prob. 7E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Prob. 9E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...

Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.2 - How many people must there be in order to assure...Ch. 8.2 - If a committee varies its meeting days, how many...Ch. 8.2 - Prob. 3E Ch. 8.2 - How many words must be chosen in order to assure...Ch. 8.2 - Prob. 5E Ch. 8.2 - If there are 6 sections of Discrete Math with a...Ch. 8.2 - Prob. 7E Ch. 8.2 - A sociologist intends to send a questionnaire to...Ch. 8.2 - Prob. 9E Ch. 8.2 - How many different pizzas can be ordered if a...Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - A restaurant offers a choice of 3 green vegetables...Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - How many 8-bit strings begin with 010 or end with...Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prove that in any nonempty list of n integers (not...Ch. 8.2 - Prob. 35E Ch. 8.2 - Suppose that there are 15 identical copies of The...Ch. 8.3 - Evaluate the numbers in Exercises 1-12. 1. 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To prove: The equation 2 C ( n , 2 ) + n 2 = C ( 2 n , 2 ) for n ≥ 2 .

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To prove: The equation 2C(n,2)+n2=C(2n,2) for n≥2.

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Chapter 8 Solutions