# How do you find the sum of Sigma 2i^2 where i is [0,5]?

Nov 10, 2017

${\sum}_{i = 0}^{5} 2 {i}^{2} = 110$

#### Explanation:

We seek:

${\sum}_{i = 0}^{5} 2 {i}^{2} = 2 {.0}^{2} + 2 {.1}^{2} + 2 {.2}^{2} + 2 {.3}^{2} + 2 {.4}^{2} + 2 {.5}^{2}$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 2 \left({0}^{2} + {1}^{2} + {2}^{2} + {3}^{2} + {4}^{2} + {5}^{2}\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 2 \left(0 + 1 + 4 + 9 + 16 + 25\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 2 \left(55\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 110$