   Chapter 13.5, Problem 4E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

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

# 3-14 Proving a formula Use mathematical induction to prove that the formula is true for all natural numbers n. 1 + 4 + 7 ⋅ ⋅ ⋅ + ( 3 n − 2 ) = n ( 3 n − 1 ) 2

To determine

To prove:

1+4+7++(3n2)=n(3n1)2

Explanation

Given:

1+4+7++(3n2)

Approach:

Use the steps to prove the statement

1. 1+4+7++(3n2)=n(3n1)2. for n=1

2. If 1+4+7++(3n2)=n(3n1)2 for n=k, then 1+4+7++(3n2)=n(3n1)2 for n=k+1 as well.

Here, n denotes natural numbers.

Calculation:

Let P(n)=n(3n1)2

For n=1

L.H.S.=1

R.H.S.=122=1

Let the statement is true for n=k, then

1+4+7++(3k2)=k(3k1)2

Let n=k+1

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