수열
등차수열
a_n = a + (n-1)d
등비수열
a_n = a \cdot r^{n-1}
수열의 합
\begin{align*}
&\sum_{k=1}^{n} k = \dfrac{n(n+1)}{2}\\[15pt]
&\sum_{k=1}^{n} k^2 = \dfrac{n(n+1)(2n+1)}{6}\\[15pt]
&\sum_{k=1}^{n} k^3 = \Bigg\{\dfrac{n(n+1)}{2}\Bigg\}^2
\end{align*}
\begin{align*}
\sum_{k=a}^{b}~k &=
\sum_{k=1}^{b}k - \sum_{k=1}^{a-1}k
\\[20pt]
&= \dfrac{b(b+1)}{2} -
\dfrac{(a-1)a}{2}
\\[20pt]
&= \dfrac{b^2 + b -a + a^2}{2}
\\[20pt]
&= \dfrac{(b+a)(b-a+1)}{2}
\\[30pt]
\sum_{k=a}^{b}~k &=
\dfrac{(b+a)(b-(a-1))}{2}
\end{align*}