# 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 - Mathematics

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 Class 11 Mathematics Textbook
Chapter 4 Principle of Mathematical Induction
Q 15 | Page 95