Calculus Examples

$\sum_{i = 1}^{4} 3 i - 2$

Step 1

Expand the series for each value of $i$ .

$3 \cdot 1 - 2 + 3 \cdot 2 - 2 + 3 \cdot 3 - 2 + 3 \cdot 4 - 2$

Step 2

Simplify.

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Multiply $3$ by $1$ .

$3 - 2 + 3 \cdot 2 - 2 + 3 \cdot 3 - 2 + 3 \cdot 4 - 2$

Subtract $2$ from $3$ .

$1 + 3 \cdot 2 - 2 + 3 \cdot 3 - 2 + 3 \cdot 4 - 2$

Multiply $3$ by $2$ .

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

Subtract $2$ from $6$ .

$1 + 4 + 3 \cdot 3 - 2 + 3 \cdot 4 - 2$

Add $1$ and $4$ .

$5 + 3 \cdot 3 - 2 + 3 \cdot 4 - 2$

Multiply $3$ by $3$ .

$5 + 9 - 2 + 3 \cdot 4 - 2$

Subtract $2$ from $9$ .

$5 + 7 + 3 \cdot 4 - 2$

Add $5$ and $7$ .

$12 + 3 \cdot 4 - 2$

Multiply $3$ by $4$ .

$12 + 12 - 2$

Subtract $2$ from $12$ .

$12 + 10$

Add $12$ and $10$ .

$22$