   Chapter 1, Problem 18P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Prove that 1 + 3 + 5 +… + (2n ‒ l ) = n2.

To determine

To prove: 1+3+5++(2n1)=n2.

Explanation

Proof:

Use Mathematical induction on n.

Statement 1+3+5++(2n1)=n2.

Base case: For n=1.

To prove that the statement is true for n=1.

(21)=12

Therefore, the statement is true for n=1.

Induction hypothesis: n=k

Assuming that the claim is true for n=k.

That is, sk=1+3+5++(2k1)=k2.

Inductive step: n=k+1

To prove the statement is true for n=k+1

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