Answer
$254$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^4 (i^4-i^3)
,$ substitute $
i
$ with the values from $
1
$ to $
4
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
1
$ to $
4
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(1^4-1^3)+(2^4-2^3)+(3^4-3^3)+(4^4-4^3)
\\\\=
(1-1)+(16-8)+(81-27)+(256-64)
\\\\=
0+8+54+192
\\\\=
254
.\end{array}
