Common Sum Formulas

Here are the formulas you'll use most often:

$\bullet$ Sum of first $n$ integers: $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$

$\bullet$ Sum of first $n$ squares: $\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$

$\bullet$ Sum of first $n$ cubes: $\sum_{i=1}^{n} i^3 = \left(\frac{n(n+1)}{2}\right)^2$

$\bullet$ Geometric series: $\sum_{i=0}^{n-1} r^i = \frac{r^n - 1}{r - 1}$ for $r \neq 1$

$\bullet$ Arithmetic series: $\sum_{i=0}^{n-1} (a + id) = \frac{n(2a + (n-1)d)}{2}$