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Chapter 4, Problem 82E

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QUESTION:

Use the results obtained in Exercise  to prove that if  is a positive integer, then \(\Gamma n=(n-1)\)!. What are the numerical values of \(\Gamma(2)\), \(\Gamma(4)\) and \(\Gamma(7)\)?

Equation Transcription:

Text Transcription:

Gamman=(n-1)

Gamma(2)

Gamma(4)

Gamma(7)

Questions & Answers

QUESTION:

Use the results obtained in Exercise  to prove that if  is a positive integer, then \(\Gamma n=(n-1)\)!. What are the numerical values of \(\Gamma(2)\), \(\Gamma(4)\) and \(\Gamma(7)\)?

Equation Transcription:

Text Transcription:

Gamman=(n-1)

Gamma(2)

Gamma(4)

Gamma(7)

ANSWER:

Step 1: Problem

(i)                 Prove Γ(n) = (n-1)!      

(ii)               Values of Γ(2), Γ(3) and Γ(4)                                  

 

Step (2):Given

Γ(n) = (n-1)Γ(n-1)                

 

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