Calculus Examples

$\sum_{k = 2}^{4} k (k - 6)$

Step 1

Simplify the summation.

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Step 1.1

Apply the distributive property.

$k \cdot k + k \cdot - 6$

Step 1.2

Multiply $k$ by $k$ .

$k^{2} + k \cdot - 6$

Step 1.3

Move $- 6$ to the left of $k$ .

$k^{2} - 6 k$

Step 1.4

Rewrite the summation.

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

Step 2

Expand the series for each value of $k$ .

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

Step 3

Simplify.

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Step 3.1

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

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

Step 3.2

Multiply $- 6$ by $2$ .

$4 - 12 + 3^{2} - 6 \cdot 3 + 4^{2} - 6 \cdot 4$

Step 3.3

Subtract $12$ from $4$ .

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

Step 3.4

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

$- 8 + 9 - 6 \cdot 3 + 4^{2} - 6 \cdot 4$

Step 3.5

Multiply $- 6$ by $3$ .

$- 8 + 9 - 18 + 4^{2} - 6 \cdot 4$

Step 3.6

Subtract $18$ from $9$ .

$- 8 - 9 + 4^{2} - 6 \cdot 4$

Step 3.7

Subtract $9$ from $- 8$ .

$- 17 + 4^{2} - 6 \cdot 4$

Step 3.8

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

$- 17 + 16 - 6 \cdot 4$

Step 3.9

Multiply $- 6$ by $4$ .

$- 17 + 16 - 24$

Step 3.10

Subtract $24$ from $16$ .

$- 17 - 8$

Step 3.11

Subtract $8$ from $- 17$ .

$- 25$