Calculus Examples

$\sum_{k = 0}^{3} 6 k^{2} - 8 k$

Step 1

Expand the series for each value of $k$ .

$6 \cdot 0^{2} - 8 \cdot 0 + 6 \cdot 1^{2} - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Raise $0$ to the power of $2$ .

$6 \cdot 0 - 8 \cdot 0 + 6 \cdot 1^{2} - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.2

Multiply $6$ by $0$ .

$0 - 8 \cdot 0 + 6 \cdot 1^{2} - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.3

Multiply $- 8$ by $0$ .

$0 + 0 + 6 \cdot 1^{2} - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.4

Add $0$ and $0$ .

$0 + 6 \cdot 1^{2} - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.5

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

$0 + 6 \cdot 1 - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.6

Multiply $6$ by $1$ .

$0 + 6 - 8 \cdot 1 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.7

Multiply $- 8$ by $1$ .

$0 + 6 - 8 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.8

Subtract $8$ from $6$ .

$0 - 2 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.9

Subtract $2$ from $0$ .

$- 2 + 6 \cdot 2^{2} - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.10

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

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

Step 2.11

Multiply $6$ by $4$ .

$- 2 + 24 - 8 \cdot 2 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.12

Multiply $- 8$ by $2$ .

$- 2 + 24 - 16 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.13

Subtract $16$ from $24$ .

$- 2 + 8 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.14

Add $- 2$ and $8$ .

$6 + 6 \cdot 3^{2} - 8 \cdot 3$

Step 2.15

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

$6 + 6 \cdot 9 - 8 \cdot 3$

Step 2.16

Multiply $6$ by $9$ .

$6 + 54 - 8 \cdot 3$

Step 2.17

Multiply $- 8$ by $3$ .

$6 + 54 - 24$

Step 2.18

Subtract $24$ from $54$ .

$6 + 30$

Step 2.19

Add $6$ and $30$ .

$36$