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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

SKILLS Plus

Discover and Prove an Inequality Find and prove an inequality relating 100 n and n 3 .

To determine

To find:

A valid inequality relating to the 100n and n3 for natural number n.

Explanation

Given:

The two sequences are,

100n and n3

Approach:

Write few terms of both the sequences, and compare the terms of the sequences.

Calculation:

First few terms of the sequence 100n are as follows,

100(1)=100

100(2)=200,

100(3)=300,

100(4)=400

100(10)=1000

100(11)=1100

100(12)=1200

First few terms of the sequence n3 are as follows,

(1)3=1<100

(2)3=8<200

(3)3=27<300

(4)3=64<400

(10)3=1000=1000

(11)3=1331>1100

(12)3=1728>1200

(50)3=125000>5000

Similarly, for nth term, n3100n, for n>10.

Check the inequality n3100n is valid for all n>10

Let P(n) denote n3100n

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Chapter 13 Solutions

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