[tex]l = \lim\limits_{n\to \infty}\frac{1+3+5+\cdots +(2n-1)}{n^2} = \lim\limits_{n\to \infty}\frac{\frac{n(1+2n-1)}{2}}{n^2} = \lim\limits_{n\to \infty} \frac{n\cdot 2n}{2n^2} = \lim\limits_{n \to \infty} \frac{2n^2}{2n^2} = \lim\limits_{n \to \infty} 1 = 1[/tex]
