   Chapter 2.2, Problem 35E

Chapter
Section
Textbook Problem

In Exercise 32 − 36 use mathematical induction to prove that the given statement is true for all positive integers n . 3 5 .           x n   <   y n , where x and y are integers with 0 < x < y

To determine

To prove: xn<yn, where x and y are integers with 0<x<y is true for all positive integers n by using mathematical induction.

Explanation

Given information:

The given statement is xn<yn, where x and y are integers with 0<x<y.

Formula used:

For all positive integers n, the statement Pn is true if,

a. Pn is true for n=1

b. The truth of Pk always implies that Pk+1 is true.

Proof:

Let Pn be the statement, “ xn<yn, where x and y are integers with 0<x<y.”

For n=1, P1 is x<y

Given that, 0<x<y

Therefore, P1 is true.

Assume that Pk is true

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