# How do you find the sum given Sigma (i-1)^2+(i+1)^3 from i=1 to 4?

Dec 16, 2017

#### Answer:

${\sum}_{i = 1}^{4} {\left(i - 1\right)}^{2} + {\left(i + 1\right)}^{3} = 238$

#### Explanation:

Let

$S = {\sum}_{i = 1}^{4} {\left(i - 1\right)}^{2} + {\left(i + 1\right)}^{3}$

Expanding we have:

$S = \left({0}^{2} + {2}^{3}\right) + \left({1}^{2} + {3}^{3}\right) + \left({2}^{2} + {4}^{3}\right) + \left({3}^{2} + {5}^{3}\right)$
$\setminus \setminus = 8 + \left(1 + 27\right) + \left(4 + 64\right) + \left(9 + 125\right)$
$\setminus \setminus = 8 + 28 + 68 + 134$
$\setminus \setminus = 238$