Answer
$700$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{k=1}^4 (k+1)^k
,$ substitute $
k
$ with the values from $
1
$ to $
4
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
k
$ with the numbers from $
1
$ to $
4
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(1+1)^1+(2+1)^2+(3+1)^3+(4+1)^4
\\\\=
(2)^1+(3)^2+(4)^3+(5)^4
\\\\=
2+9+64+625
\\\\=
700
.\end{array}
