Write a Proof by Mathematical Induction of the Statement $1^{2}+3^{2}+5^{2}+\ldots+(2 n-1)^{2}=\frac{n(2 n-1)(2 n+1)}{3}$

question 94

Essay

Write a proof by mathematical induction of the statement:
$1^{2}+3^{2}+5^{2}+\ldots+(2 n-1)^{2}=\frac{n(2 n-1)(2 n+1)}{3}$

---

Definitions:

Express Warranty

An explicit guarantee by a seller regarding the condition, quality, or performance of the product being sold.

Consumer Good

Any tangible commodity produced and subsequently purchased to satisfy the current wants and perceived needs of the buyer.

Warranty Of Merchantability

An implied assurance that goods are sufficiently free from defect, fit for the general purpose for which they are sold.

Implied Warranty

A legal concept that guarantees a product will meet certain minimum standards of quality and functionality implied by law, even if not expressly stated.