Calculus Examples

$\sum_{k = 3}^{6} - 5 k + 20$

Step 1

Expand the series for each value of $k$ .

$- 5 \cdot 3 + 20 - 5 \cdot 4 + 20 - 5 \cdot 5 + 20 - 5 \cdot 6 + 20$

Step 2

Simplify.

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Step 2.1

Multiply $- 5$ by $3$ .

$- 15 + 20 - 5 \cdot 4 + 20 - 5 \cdot 5 + 20 - 5 \cdot 6 + 20$

Step 2.2

Add $- 15$ and $20$ .

$5 - 5 \cdot 4 + 20 - 5 \cdot 5 + 20 - 5 \cdot 6 + 20$

Step 2.3

Multiply $- 5$ by $4$ .

$5 - 20 + 20 - 5 \cdot 5 + 20 - 5 \cdot 6 + 20$

Step 2.4

Add $- 20$ and $20$ .

$5 + 0 - 5 \cdot 5 + 20 - 5 \cdot 6 + 20$

Step 2.5

Add $5$ and $0$ .

$5 - 5 \cdot 5 + 20 - 5 \cdot 6 + 20$

Step 2.6

Multiply $- 5$ by $5$ .

$5 - 25 + 20 - 5 \cdot 6 + 20$

Step 2.7

Add $- 25$ and $20$ .

$5 - 5 - 5 \cdot 6 + 20$

Step 2.8

Subtract $5$ from $5$ .

$0 - 5 \cdot 6 + 20$

Step 2.9

Multiply $- 5$ by $6$ .

$0 - 30 + 20$

Step 2.10

Add $- 30$ and $20$ .

$0 - 10$

Step 2.11

Subtract $10$ from $0$ .

$- 10$