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# Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1^2 + 3^2 + 5^2 + ... + (2n -1)^2 = (N(2n - 1) (2n + 1))/3 - CBSE (Arts) Class 11 - Mathematics

ConceptPrinciple of Mathematical Induction

#### Question

Prove the following by using the principle of mathematical induction for all n ∈ N

1^2 + 3^2 + 5^2 + ... + (2n -1)^2 = (n(2n - 1) (2n + 1))/3

#### Solution

Let the given statement be P(n), i.e.,

Thus, P(k + 1) is true whenever P(k) is true.

Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 4: Principle of Mathematical Induction
Q: 15 | Page no. 95

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Solution Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1^2 + 3^2 + 5^2 + ... + (2n -1)^2 = (N(2n - 1) (2n + 1))/3 Concept: Principle of Mathematical Induction.
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