Calculus Examples

$\sum_{i = 0}^{3} 3 i - 7 j$

Step 1

Expand the series for each value of $i$ .

$3 \cdot 0 - 7 j + 3 \cdot 1 - 7 j + 3 \cdot 2 - 7 j + 3 \cdot 3 - 7 j$

Step 2

Substitute the values back and simplify $3 \cdot 0 - 7 j + 3 \cdot 1 - 7 j + 3 \cdot 2 - 7 j + 3 \cdot 3 - 7 j$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $3$ by $0$ .

$0 - 7 j + 3 \cdot 1 - 7 j + 3 \cdot 2 - 7 j + 3 \cdot 3 - 7 j$

Step 2.1.2

Multiply $3$ by $1$ .

$0 - 7 j + 3 - 7 j + 3 \cdot 2 - 7 j + 3 \cdot 3 - 7 j$

Step 2.1.3

Multiply $3$ by $2$ .

$0 - 7 j + 3 - 7 j + 6 - 7 j + 3 \cdot 3 - 7 j$

Step 2.1.4

Multiply $3$ by $3$ .

$0 - 7 j + 3 - 7 j + 6 - 7 j + 9 - 7 j$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $7 j$ from $0$ .

$- 7 j + 3 - 7 j + 6 - 7 j + 9 - 7 j$

Step 2.2.2

Subtract $7 j$ from $- 7 j$ .

$- 14 j + 3 + 6 - 7 j + 9 - 7 j$

Step 2.2.3

Subtract $7 j$ from $- 14 j$ .

$- 21 j + 3 + 6 + 9 - 7 j$

Step 2.2.4

Subtract $7 j$ from $- 21 j$ .

$- 28 j + 3 + 6 + 9$

Step 2.2.5

Simplify by adding numbers.

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Step 2.2.5.1

Add $3$ and $6$ .

$- 28 j + 9 + 9$

Step 2.2.5.2

Add $9$ and $9$ .

$- 28 j + 18$