Calculus Examples

$\sum_{m = 1}^{4} 8 k - 6 m$

Step 1

Expand the series for each value of $m$ .

$8 k - 6 \cdot 1 + 8 k - 6 \cdot 2 + 8 k - 6 \cdot 3 + 8 k - 6 \cdot 4$

Step 2

Substitute the values back and simplify $8 k - 6 \cdot 1 + 8 k - 6 \cdot 2 + 8 k - 6 \cdot 3 + 8 k - 6 \cdot 4$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 6$ by $1$ .

$8 k - 6 + 8 k - 6 \cdot 2 + 8 k - 6 \cdot 3 + 8 k - 6 \cdot 4$

Step 2.1.2

Multiply $- 6$ by $2$ .

$8 k - 6 + 8 k - 12 + 8 k - 6 \cdot 3 + 8 k - 6 \cdot 4$

Step 2.1.3

Multiply $- 6$ by $3$ .

$8 k - 6 + 8 k - 12 + 8 k - 18 + 8 k - 6 \cdot 4$

Step 2.1.4

Multiply $- 6$ by $4$ .

$8 k - 6 + 8 k - 12 + 8 k - 18 + 8 k - 24$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $8 k$ and $8 k$ .

$16 k - 6 - 12 + 8 k - 18 + 8 k - 24$

Step 2.2.2

Add $16 k$ and $8 k$ .

$24 k - 6 - 12 - 18 + 8 k - 24$

Step 2.2.3

Add $24 k$ and $8 k$ .

$32 k - 6 - 12 - 18 - 24$

Step 2.2.4

Simplify by subtracting numbers.

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Step 2.2.4.1

Subtract $12$ from $- 6$ .

$32 k - 18 - 18 - 24$

Step 2.2.4.2

Subtract $18$ from $- 18$ .

$32 k - 36 - 24$

Step 2.2.4.3

Subtract $24$ from $- 36$ .

$32 k - 60$