Calculus Examples

$\sum_{k = 0}^{2} 2 k + 2$

Step 1

Expand the series for each value of $k$ .

$2 \cdot 0 + 2 + 2 \cdot 1 + 2 + 2 \cdot 2 + 2$

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $0$ .

$0 + 2 + 2 \cdot 1 + 2 + 2 \cdot 2 + 2$

Step 2.2

Add $0$ and $2$ .

$2 + 2 \cdot 1 + 2 + 2 \cdot 2 + 2$

Step 2.3

Multiply $2$ by $1$ .

$2 + 2 + 2 + 2 \cdot 2 + 2$

Step 2.4

Add $2$ and $2$ .

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

Step 2.5

Add $2$ and $4$ .

$6 + 2 \cdot 2 + 2$

Step 2.6

Multiply $2$ by $2$ .

$6 + 4 + 2$

Step 2.7

Add $4$ and $2$ .

$6 + 6$

Step 2.8

Add $6$ and $6$ .

$12$

$12$

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