Answer
$1,240$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
\displaystyle\sum_{i=1}^{15} i^2
,$ use the properties of summation.
$\bf{\text{Solution Details:}}$
Using a property of the summation which is given by $\displaystyle\sum_{i=1}^n i^2=\dfrac{n(n+1)(2n+1)}{6},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{15(15+1)(2(15)+1)}{6}
\\\\=
\dfrac{15(16)(30+1)}{6}
\\\\=
\dfrac{\cancel3\cdot5(\cancel2\cdot8)(31)}{\cancel2\cancel3}
\\\\=
5(8)(31)
\\\\=
1,240
.\end{array}
