Calculus Examples

$\sum_{k = 15}^{18} {(- 1)}^{k} (3 k)$

Step 1

Expand the series for each value of $k$ .

${(- 1)}^{15} (3 \cdot 15) + {(- 1)}^{16} (3 \cdot 16) + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2

Simplify.

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Step 2.1

Raise $- 1$ to the power of $15$ .

$- 1 (3 \cdot 15) + {(- 1)}^{16} (3 \cdot 16) + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.2

Multiply $3$ by $15$ .

$- 1 \cdot 45 + {(- 1)}^{16} (3 \cdot 16) + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.3

Multiply $- 1$ by $45$ .

$- 45 + {(- 1)}^{16} (3 \cdot 16) + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.4

Raise $- 1$ to the power of $16$ .

$- 45 + 1 (3 \cdot 16) + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.5

Multiply $3$ by $16$ .

$- 45 + 1 \cdot 48 + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.6

Multiply $1$ by $48$ .

$- 45 + 48 + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.7

Add $- 45$ and $48$ .

$3 + {(- 1)}^{17} (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.8

Raise $- 1$ to the power of $17$ .

$3 - 1 (3 \cdot 17) + {(- 1)}^{18} (3 \cdot 18)$

Step 2.9

Multiply $3$ by $17$ .

$3 - 1 \cdot 51 + {(- 1)}^{18} (3 \cdot 18)$

Step 2.10

Multiply $- 1$ by $51$ .

$3 - 51 + {(- 1)}^{18} (3 \cdot 18)$

Step 2.11

Subtract $51$ from $3$ .

$- 48 + {(- 1)}^{18} (3 \cdot 18)$

Step 2.12

Raise $- 1$ to the power of $18$ .

$- 48 + 1 (3 \cdot 18)$

Step 2.13

Multiply $3$ by $18$ .

$- 48 + 1 \cdot 54$

Step 2.14

Multiply $1$ by $54$ .

$- 48 + 54$

Step 2.15

Add $- 48$ and $54$ .

$6$