Sigma Notation
The sum of \(n\) terms \(a_1, a_2, \ldots, a_n\) written as
$$
\sum_{i=1}^n a_i = a_1 + a_2 + a_3 + \cdots + a_n
$$
where \(i\) is the index of summation, \(a_i\) is the \(i\)th term of the sum, and the upper and lower bounds of summation are \(n\) and 1.
The sum of \(n\) terms \(a_1, a_2, \ldots, a_n\) written as
$$
\sum_{i=1}^n a_i = a_1 + a_2 + a_3 + \cdots + a_n
$$
where \(i\) is the index of summation, \(a_i\) is the \(i\)th term of the sum, and the upper and lower bounds of summation are \(n\) and 1.
Summation Formulas
- \(\displaystyle \sum_{i=1}^n c = cn\)
- \(\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}{2}\)
- \(\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}\)
- \(\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}{4}\)