Calculus Examples

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

Step 1

Expand the series for each value of $k$ .

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

Step 2

Simplify.

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Step 2.1

Add $1$ and $1$ .

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

Step 2.2

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

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

Step 2.3

Multiply $1$ by $1$ .

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

Step 2.4

Add $2$ and $1$ .

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

Step 2.5

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

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

Step 2.6

Multiply $- 1$ by $2$ .

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

Step 2.7

Subtract $2$ from $1$ .

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

Step 2.8

Add $3$ and $1$ .

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

Step 2.9

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

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

Step 2.10

Multiply $1$ by $3$ .

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

Step 2.11

Add $- 1$ and $3$ .

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

Step 2.12

Add $4$ and $1$ .

$2 + {(- 1)}^{5} \cdot 4$

Step 2.13

Raise $- 1$ to the power of $5$ .

$2 - 1 \cdot 4$

Step 2.14

Multiply $- 1$ by $4$ .

$2 - 4$

Step 2.15

Subtract $4$ from $2$ .

$- 2$