Answer
$3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{k=1}^6 (-1)^k\cdot k
,$ substitute $
k
$ with the values from $
1
$ to $
6
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
k
$ with the numbers from $
1
$ to $
6
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
[(-1)^1\cdot 1]+[(-1)^2\cdot 2]+[(-1)^3\cdot 3]+[(-1)^4\cdot 4]+[(-1)^5\cdot 5]+[(-1)^6\cdot 6]
\\\\=
[(-1)\cdot 1]+[(1)\cdot 2]+[(-1)\cdot 3]+[(1)\cdot 4]+[(-1)\cdot 5]+[(1)\cdot 6]
\\\\=
-1+2-3+4-5+6
\\\\=
3
.\end{array}
