Revision sheet

Arithmetic series

• $\displaystyle\sum_{k=p}^{q}$ has $q - p + 1$ terms.
• $S_n = \dfrac{n(a_1 + a_n)}{2}$.
• $1 + 2 + \dots + n = \dfrac{n(n + 1)}{2}$.

Watch out: count the terms with $+1$.

Finite geometric series

• $S_n = a_1\,\dfrac{r^n - 1}{r - 1}$.
• $n$ is the number of terms; the power is $r^n$.

Watch out: the last term is $a_1 r^{\,n-1}$, but the sum uses $r^n$.