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Let r be a real number and let k be an integer. We then define the binomial coefficient () by r(r-1) (r-k+1) O-F k! if k 21 if k=0 if k ≤ -1. 1. For any real number r and any integer r #k, show that a) ()=(²¹), and b) () = (-1)k (r+k-1). Hint: use the definition of () from Page 137.

Let r be a real number and let k be an integer. We then define the binomial coefficient () by r(r-1) (r-k+1) O-F k! if k 21 if k=0 if k ≤ -1. 1. For any real number r and any integer r #k, show that a) ()=(²¹), and b) () = (-1)k (r+k-1). Hint: use the definition of () from Page 137.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Letr be a real number and let k be an integer. We then define the binomial coefficient () by (Q)-{} r(r-1)(r-k+1) k! if k 21 if k = 0 if k ≤ -1. CC 1. For any real number r and any integer r #k, show that a) ()=(¹), and b) (77) = (-1)k (r+k-1). Hint: use the definition of() from Page 137. -k
Transcribed Image Text:Letr be a real number and let k be an integer. We then define the binomial coefficient () by (Q)-{} r(r-1)(r-k+1) k! if k 21 if k = 0 if k ≤ -1. CC 1. For any real number r and any integer r #k, show that a) ()=(¹), and b) (77) = (-1)k (r+k-1). Hint: use the definition of() from Page 137. -k
Expert Solution
Step 1

Given, r is a real number and k is an integer 

The Binomial Coefficient rk by

rk= r (r - 1) --- (r - k + 1)k !            if k ≥ 11                                                            if k = 00                                                            if k ≤ -1

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