Calculus Examples

$4 \sum_{k = 3}^{6} - k^{2} + 2 k$

Step 1

Expand the series for each value of $k$ .

$4 (- 3^{2} + 2 \cdot 3 - 4^{2} + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2

Simplify.

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Step 2.1

Raise $3$ to the power of $2$ .

$4 (- 1 \cdot 9 + 2 \cdot 3 - 4^{2} + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.2

Multiply $- 1$ by $9$ .

$4 (- 9 + 2 \cdot 3 - 4^{2} + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.3

Multiply $2$ by $3$ .

$4 (- 9 + 6 - 4^{2} + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.4

Add $- 9$ and $6$ .

$4 (- 3 - 4^{2} + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.5

Raise $4$ to the power of $2$ .

$4 (- 3 - 1 \cdot 16 + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.6

Multiply $- 1$ by $16$ .

$4 (- 3 - 16 + 2 \cdot 4 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.7

Multiply $2$ by $4$ .

$4 (- 3 - 16 + 8 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.8

Add $- 16$ and $8$ .

$4 (- 3 - 8 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.9

Subtract $8$ from $- 3$ .

$4 (- 11 - 5^{2} + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.10

Raise $5$ to the power of $2$ .

$4 (- 11 - 1 \cdot 25 + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.11

Multiply $- 1$ by $25$ .

$4 (- 11 - 25 + 2 \cdot 5 - 6^{2} + 2 \cdot 6)$

Step 2.12

Multiply $2$ by $5$ .

$4 (- 11 - 25 + 10 - 6^{2} + 2 \cdot 6)$

Step 2.13

Add $- 25$ and $10$ .

$4 (- 11 - 15 - 6^{2} + 2 \cdot 6)$

Step 2.14

Subtract $15$ from $- 11$ .

$4 (- 26 - 6^{2} + 2 \cdot 6)$

Step 2.15

Raise $6$ to the power of $2$ .

$4 (- 26 - 1 \cdot 36 + 2 \cdot 6)$

Step 2.16

Multiply $- 1$ by $36$ .

$4 (- 26 - 36 + 2 \cdot 6)$

Step 2.17

Multiply $2$ by $6$ .

$4 (- 26 - 36 + 12)$

Step 2.18

Add $- 36$ and $12$ .

$4 (- 26 - 24)$

Step 2.19

Subtract $24$ from $- 26$ .

$4 \cdot - 50$

Step 2.20

Multiply $4$ by $- 50$ .

$- 200$