# How do you find the sum of the series 2n^2+1 from n=0 to 4?

Jan 26, 2017

${\sum}_{n = 0}^{4} 2 {n}^{2} + 1 = \left(2 {\left(0\right)}^{2} + 1\right) + \left(2 {\left(1\right)}^{2} + 1\right) + \left(2 {\left(2\right)}^{2} + 1\right) + \left(2 {\left(3\right)}^{2} + 1\right) + \left(2 {\left(4\right)}^{2} + 1\right)$
$\setminus \setminus \setminus = \left(0 + 1\right) + \left(2 + 1\right) + \left(8 + 1\right) + \left(18 + 1\right) + \left(32 + 1\right)$
$\setminus \setminus \setminus = 60 + 6$
$\setminus \setminus \setminus = 65$