Precalculus Examples

$\sum_{j = 1}^{4} {(- 1)}^{j} j$

Step 1

Expand the series for each value of $j$ .

${(- 1)}^{1} \cdot 1 + {(- 1)}^{2} \cdot 2 + {(- 1)}^{3} \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Raise $- 1$ to the power of $1$ .

$- 1 \cdot 1 + {(- 1)}^{2} \cdot 2 + {(- 1)}^{3} \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2.2

Multiply $- 1$ by $1$ .

$- 1 + {(- 1)}^{2} \cdot 2 + {(- 1)}^{3} \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2.3

Raise $- 1$ to the power of $2$ .

$- 1 + 1 \cdot 2 + {(- 1)}^{3} \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2.4

Multiply $1$ by $2$ .

$- 1 + 2 + {(- 1)}^{3} \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2.5

Add $- 1$ and $2$ .

$1 + {(- 1)}^{3} \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2.6

Raise $- 1$ to the power of $3$ .

$1 - 1 \cdot 3 + {(- 1)}^{4} \cdot 4$

Step 2.7

Multiply $- 1$ by $3$ .

$1 - 3 + {(- 1)}^{4} \cdot 4$

Step 2.8

Subtract $3$ from $1$ .

$- 2 + {(- 1)}^{4} \cdot 4$

Step 2.9

Raise $- 1$ to the power of $4$ .

$- 2 + 1 \cdot 4$

Step 2.10

Multiply $1$ by $4$ .

$- 2 + 4$

Step 2.11

Add $- 2$ and $4$ .

$2$