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Q18E

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Discrete Mathematics and its Applications

Found in: Page 370

Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Prove that Algorithm 1 for computing n! when n is a nonnegative integer is correct.

The required algorithm is proved by induction.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Base case

The algorithm is for when n is non-negative, the base case is .

factorial (0) = 0!

= 1

Step 2: Prove that Algorithm 1 for computing n!

By induction hypothesis,

$\begin{aligned} factorial (k) = k! \\ factorial (k + 1) = (k + 1) \cdot factorial (k) \\ = (k + 1) \cdot k! \\ = (k + 1)! \end{aligned}$

Therefore, the required algorithm is proved by induction.

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Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Prove that Algorithm 1 for computing n! when n is a nonnegative integer is correct.

Step by Step Solution

Step 1: Base case

Step 2: Prove that Algorithm 1 for computing n!

Most popular questions for Math Textbooks

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Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Prove that Algorithm 1 for computing n! when n is a nonnegative integer is correct.

Step by Step Solution

Step 1: Base case

Step 2: Prove that Algorithm 1 for computing n!

Most popular questions for Math Textbooks

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