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1 1 1 1 2 1 of finding the coefficients are equivalent

1 1 1 1 2 1 of finding the coefficients are equivalent

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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B) Use (k ) = (G") + (k) and mathematical induction to prove the binomial formula n+ B) Use and mathematical induction to prove the binomial formula (z + y)" = (; -*y~-+ "yn-k k=0
Transcribed Image Text:B) Use (k ) = (G") + (k) and mathematical induction to prove the binomial formula n+ B) Use and mathematical induction to prove the binomial formula (z + y)" = (; -*y~-+ "yn-k k=0
The binomial theorem says that (x + y)" x*yn-k k=0 n! where the coefficients are given by k) k!(n – k)! A) We also know that the coefficients of the binomial theorem can be found with the help of Pascals triangle: n = 0: 1 n = 1: 1 1 п 3 2: 1 2 1 Show that these two ways of finding the coefficients are equivalent by showing the formula (":') - (,".) - () n k .(":) - (.".) · ) (3) +1 k B) Use and mathematical induction to prove the binomial formula
Transcribed Image Text:The binomial theorem says that (x + y)" x*yn-k k=0 n! where the coefficients are given by k) k!(n – k)! A) We also know that the coefficients of the binomial theorem can be found with the help of Pascals triangle: n = 0: 1 n = 1: 1 1 п 3 2: 1 2 1 Show that these two ways of finding the coefficients are equivalent by showing the formula (":') - (,".) - () n k .(":) - (.".) · ) (3) +1 k B) Use and mathematical induction to prove the binomial formula
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