A collection of random formulas. This serves partly as my notes, and partly as part of my website. idk why this exists
To find a particular term in the series, assuming that the term number is x, replace ∞ with x-1, which works for everything except the first term which is of course 3.
\[ 3+\sum_{n=1}^{\infty}\left(-1\right)^{n-1}\frac{4}{2n\cdot\left(2n+1\right)\cdot\left(2n+2\right)} \]
\[ x = -\frac{b}{2a}\pm\sqrt{-\frac{c}{a}+\left(\frac{b}{2a}\right)^2} \]
\[ y=f'\left(x_1\right)\left(x-x_{1}\right)+f\left(x_{1}\right) \]
Assuming that the indefinite integral is \(f(x)\):
\[ \int_{b}^{a}=f(b)-f(a) \]