Below are solutions to the practice equations. There are multiple ways to express some of the equations, so your solutions do not need to exactly match the answers given.

1. [latex]x^2 + y^2 = 1[/latex]
   [‌latex]x^2 + y^2 = 1[/latex]
2. [latex]T = 2 \pi \sqrt{\frac{m}{k}}[/latex]
   [‌latex]T = 2 \pi \sqrt{\frac{m}{k}}[/latex]
3. [latex]F_g = \frac{G m_1 m_2}{r^2}[/latex]
   [‌latex]F_g = \frac{Gm_1 m_2}{r^2}[/latex]
4. [latex]\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}[/latex]
   [‌latex]\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}[/latex]
   If you want the sum to have the limits above and below, like you see in most textbooks, you can use the command \displaystyle.
   [latex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}[/latex]
   [‌latex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}[/latex]
5. The equation is missing a bracket to close the numerator of the fraction, shown in bold below.
   [‌latex] x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a} [/latex]