   Chapter 9.7, Problem 12ES ### 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
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# Use Pascal’s formula repeatedly to derive a formula for ( r n + 3 ) in term of values of ( k n ) with k ≤ r . (Asssume n and r are integers with n ≥ r ≥ 3 .)

To determine

To derive a formula for ( n+3r) in terms of (nk) with kr using Pascal’s formula repeatedly.

Explanation

Given information:

The expression ( n+3r).

Concept used:

Pascal’s formula; ( n+1r)=(n r1)+(nr)

Calculation:

( n+3 r )=( n+2 r1 )+( n+2 r )=[( n+1 r2 )+( n+1 r1 )]+[( n+1 r1 )+( n+1 r )]=[{( n r3 )+( n r2 )}+{( n

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