5.2 | Area


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.
Summation Formulas

  1. \(\displaystyle \sum_{i=1}^n c = cn\)
  2. \(\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}{2}\)
  3. \(\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}\)
  4. \(\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}{4}\)

E 5.2 Exercises