   Chapter 9.7, Problem 9ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Justify the equations 6-9 either by deriving them from formulas in Example 9.7.1 or by direct computation from Theorem 9.5.1. Assume m,n,k, and r are integers. ( 2 n 2 ( n + 1 ) ) = ( n + 1 ) ( 2 n + 1 ) ,   for   n ≥ 0

To determine

Use the formula (nr)=n!r!(nr)! to prove algebraically that ( 2( n+1 ) 2n)=(n+1)(2n+1).

Explanation

Given information:

( 2( n+1 ) 2n)=(n+1)(2n+1) for n0.

Assume n is integer.

Calculation:

Let us consider the theorem (nr)=n!r!(nr)!.

Consider n=2(n+1) and r=2n

( 2( n+1 ) 2n)=(2( n+1))! [(2( n+1))2n]!(2n)!

Above statement is valid only if; 2n0, that is n0

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