   Chapter 9.7, Problem 13ES ### 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

# Use Pascal’s formula to prove by mathematical induction that if n is an integer and n ≥ 1 , then ∑ i = 2 n + 1 ( 2 i ) = ( 2 2 ) + ( 2 3 ) + ... + ( 2 n + 1 ) ( 3 n + 2 )

To determine

To prove the formula i=2n+1(i2)=(22)+(32)++( n+12)=( n+23) if n is an integer and n1 using mathematical induction.

Explanation

Given:

The formula to prove i=2n+1(i2)=(22)+(32)++( n+12)=( n+23).

Concept used:

Pascal’s formula; ( n+1r)=(n r1)+(nr)

Proof:

Let’s show that the result is true for n=1 ;

i=22(i2)=(22)=2!0!2!=1

( 1+23)=3!0!3!=1

Therefore, i=22(i2)=( 1+23).

Hence, the result is true for n=1.

Now assume that the result us true for n=m.

i=2m+1(i2)=(22)+(32)++( m+12)=( m+2

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