Explanation Given information: The expansion, ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) ( 3 4 ) 4 + ( 5 4 ) ( 3 4 ) 5 . Formula used: Binomial Theorem: Let x and y be real numbers. For any positive integer n , ( x + y ) n = ( n 0 ) x n + ( n 1 ) y x n − 1 + ...... + ( n j ) y j x n − j + .... + ( n n ) y n = ∑ j = 0 n ( n j ) y j x n − j Calculation: Now use binomial theorem, Comparing the expansion ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) ( 3 4 ) 4 + ( 5 4 ) ( 3 4 ) 5 with the general expansion ( n 0 ) x n + ( n 1 ) y x n − 1 + ...... + ( n j ) y j x n − j + .... + ( n n ) y n , the values are x = 1 4 , y = 3 4 , n = 5 . Now using binomial theorem, ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) ( 3 4 ) 4 + ( 5 4 ) ( 3 4 ) 5 = ( 1 4 + 3 4 ) 5 ⇒ ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) + ( 5 2

Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)

10th Edition

ISBN: 9780321978981

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 12.5, Problem 49AYU

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To calculate: The value of (50)(14)5+(51)(14)4(34)+(52)(14)3(34)2+(53)(14)2(34)3+(54)(14)(34)4+(54)(34)5

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Chapter 12.5, Problem 48AYU

Chapter 12.5, Problem 50AYU

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Chapter 12 Solutions

Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)

Ch. 12.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 12.1 - True or False A function is a relation between two...Ch. 12.1 - Prob. 3AYU Ch. 12.1 - True or False The notation a 5 represents the...Ch. 12.1 - True or False If is am integer, then Ch. 12.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 12.1 - The notation a 1 + a 2 + a 3 ++ a n = k=1 n a k...Ch. 12.1 - Prob. 8AYU Ch. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - Prob. 10AYU

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The value of ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) ( 3 4 ) 4 + ( 5 4 ) ( 3 4 ) 5

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To calculate: The value of (50)(14)5+(51)(14)4(34)+(52)(14)3(34)2+(53)(14)2(34)3+(54)(14)(34)4+(54)(34)5

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