Prove by mathematical induction that $\displaystyle\sum_{r=1}^{n}(2r-1)=n^2$ for every \(n\in

Question

Prove by mathematical induction that $\displaystyle\sum_{r=1}^{n}(2r-1)=n^2$ for every $n\in\mathbb Z^+$.

Accepted Answer

$\displaystyle\sum_{r=1}^{n}(2r-1)=n^2$

Sum of the First Odd Integers