Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Textbook Question

Chapter 8.4, Problem 44E

Use generating functions to prove Pascal’s identity: C ( n , r ) = C ( n − 1 , r ) + C ( n − 1 , r − 1 ) when n and r are positive integers with r < n .[Hint: Use the identity

( 1 + x ) n = ( 1 + x ) n − 1 + x ( 1 + x ) n − 1 .]

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Chapter 8.4, Problem 43E

Chapter 8.4, Problem 45E

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Chapter 8 Solutions

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

Ch. 8.1 - Use mathematical induction to verify the formula...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - A vending machine dispensing books of stamps...Ch. 8.1 - A country uses as currency coins with values of 1...Ch. 8.1 - How many was are there to pay a bill of 17 pesos...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...Ch. 8.1 - a) Find a recurrence relation for the number of...

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Use generating functions to prove Pascal’s identity: C ( n , r ) = C ( n − 1 , r ) + C ( n − 1 , r − 1 ) when n and r are positive integers with r &lt; n .[ Hint: Use the identity ( 1 + x ) n = ( 1 + x ) n − 1 + x ( 1 + x ) n − 1 .]

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Chapter 8 Solutions

Use generating functions to prove Pascal’s identity: C ( n , r ) = C ( n − 1 , r ) + C ( n − 1 , r − 1 ) when n and r are positive integers with r < n .[ Hint: Use the identity ( 1 + x ) n = ( 1 + x ) n − 1 + x ( 1 + x ) n − 1 .]