summation
Given a sequence \( \left ( a_{n} \right ) \), then we define
\( \sum_{i = 1}^{n} := a_{1} + a_{2} + \ldots + a_{n} \)
constant can be factored
Suppose \( c \in \mathbb{R} \), then \( \sum_{i = 1}^{n} c a_{i} = c \sum_{i = 1}^{n} a_{i} \)
TODO
TODO
Suppose \( \left ( a_{n} \right ) \) and \( \left ( b_{n} \right ) \) are sequences, then
\( \sum_{i = 1}^{n} \left ( a_{i} \pm b_{i} \right ) = \sum_{i = 1}^{n} a_{i} \pm \sum_{i = 1}^{n} b_{i} \)
TODO
sum of consecutive integers
\( \sum_{k = 1}^{n} k = \frac{n \cdot \left ( n + 1 \right )}{2} \)
TODO