Answer
$\Sigma^{20}_{i=1} (i+1)^{2}$ =3310
Work Step by Step
$\Sigma^{20}_{i=1} (i+1)^{2}$ = $\Sigma^{20}_{i=1} (i^{2}+2i+1)$
=$\Sigma^{20}_{i=1}i^{2} + \Sigma^{20}_{i=1} 2i +\Sigma^{20}_{i=1} 1$
Using the properties of summation $\Sigma^{n}_{i=1} i=\frac{n(n+1)}{2}$ and $\Sigma^{n}_{i=1} i^{2}=\frac{n(n+1)(2n+1)}{6}$,
$\Sigma^{20}_{i=1}i^{2} + \Sigma^{20}_{i=1} 2i +\Sigma^{20}_{i=1} 1$=$\frac{20(21)(41)}{6}+2\frac{20(21)}{2} +20$
=3310
