   Chapter 11.4, Problem 33ES ### 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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# Prove each of the statements in 32—37, assuming n is an integer variable that takes positive integer values. Use identities from Section 5.2 as needed.33. 4 + 4 2 + 4 3 + ⋯ + 4 n is Θ ( 4 n ) .

To determine

To prove the following statement assuming n as integer variables that takes positive integer values.

Explanation

Given information:

4+42+43+........+4n=Θ(4n)

Calculation:

Simplifying the given expression as follows-

4+42+43+........+4n=4(1+4+42+.....+4n1)=4[ 4 n1+1141]{applying the formula of sum of n terms of GP i.er=0nrn= r n+1 1 r1;n0}=44n13=43(4n1)

It is given that n is positive integer that means −

4+42+43+........+4n4n{n>0}....(1)

Also,

4+42+43+

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