Calculus Examples

$\sum_{k = 1}^{4} {(- 1)}^{k} (k + 11)$

Step 1

Expand the series for each value of $k$ .

${(- 1)}^{1} (1 + 11) + {(- 1)}^{2} (2 + 11) + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2

Simplify.

Tap for more steps...

Step 2.1

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

$- 1 (1 + 11) + {(- 1)}^{2} (2 + 11) + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.2

Add $1$ and $11$ .

$- 1 \cdot 12 + {(- 1)}^{2} (2 + 11) + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.3

Multiply $- 1$ by $12$ .

$- 12 + {(- 1)}^{2} (2 + 11) + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.4

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

$- 12 + 1 (2 + 11) + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.5

Add $2$ and $11$ .

$- 12 + 1 \cdot 13 + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.6

Multiply $1$ by $13$ .

$- 12 + 13 + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.7

Add $- 12$ and $13$ .

$1 + {(- 1)}^{3} (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.8

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

$1 - 1 (3 + 11) + {(- 1)}^{4} (4 + 11)$

Step 2.9

Add $3$ and $11$ .

$1 - 1 \cdot 14 + {(- 1)}^{4} (4 + 11)$

Step 2.10

Multiply $- 1$ by $14$ .

$1 - 14 + {(- 1)}^{4} (4 + 11)$

Step 2.11

Subtract $14$ from $1$ .

$- 13 + {(- 1)}^{4} (4 + 11)$

Step 2.12

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

$- 13 + 1 (4 + 11)$

Step 2.13

Add $4$ and $11$ .

$- 13 + 1 \cdot 15$

Step 2.14

Multiply $1$ by $15$ .

$- 13 + 15$

Step 2.15

Add $- 13$ and $15$ .

$2$