Precalculus Examples

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

Step 1

Expand the series for each value of

$k$ .

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

Step 2

Simplify.

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Step 2.1

Multiply

$2$ by

$1$ .

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

Step 2.2

Multiply

$2$ by

$2$ .

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

Step 2.3

Add

$2$ and

$4$ .

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

Step 2.4

Multiply

$2$ by

$3$ .

$6 + 6 + 2 \cdot 4$

Step 2.5

Add

$6$ and

$6$ .

$12 + 2 \cdot 4$

Step 2.6

Multiply

$2$ by

$4$ .

$12 + 8$

Step 2.7

Add

$12$ and

$8$ .

$20$

$20$

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

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