Calculus Examples

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

Step 1

Expand the series for each value of $i$ .

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

Step 2

Simplify.

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Multiply $2$ by $1$ .

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

Multiply $2$ by $2$ .

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

Add $2$ and $4$ .

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

Multiply $2$ by $3$ .

$6 + 6 + 2 \cdot 4$

Add $6$ and $6$ .

$12 + 2 \cdot 4$

Multiply $2$ by $4$ .

$12 + 8$

Add $12$ and $8$ .

$20$

$20$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$