# How do you find the sum of the series i from i=1 to 18?

Nov 13, 2016

${\sum}_{i = 1}^{18} i = 171$

#### Explanation:

Using the standard results:
${\sum}_{r = 1}^{n} r = \frac{1}{2} n \left(n + 1\right)$

We have;

${\sum}_{i = 1}^{18} i = \frac{1}{2} \left(18\right) \left(18 + 1\right)$
$\therefore {\sum}_{i = 1}^{18} i = \frac{1}{2} \left(18\right) \left(19\right)$
$\therefore {\sum}_{i = 1}^{18} i = 171$