# How do you use the properties of summation to evaluate the sum of Sigma 2i from i=1 to 20?

Jan 5, 2017

${\sum}_{i = 1}^{20} \left(2 i\right) = 420$

#### Explanation:

Use the standard summation formula

${\sum}_{r = 1}^{n} r = \frac{1}{2} n \left(n + 1\right)$

${\sum}_{i = 1}^{20} \left(2 i\right) = 2 {\sum}_{i = 1}^{20} i$
$\text{ } = 2 \cdot \frac{1}{2} \left(20\right) \left(21\right)$
$\text{ } = 420$