Precalculus Examples

$\sum_{k = 3}^{4} k^{2} - 2 k$

Step 1

Expand the series for each value of $k$ .

$3^{2} - 2 \cdot 3 + 4^{2} - 2 \cdot 4$

Step 2

Simplify.

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Step 2.1

Raise $3$ to the power of $2$ .

$9 - 2 \cdot 3 + 4^{2} - 2 \cdot 4$

Step 2.2

Multiply $- 2$ by $3$ .

$9 - 6 + 4^{2} - 2 \cdot 4$

Step 2.3

Subtract $6$ from $9$ .

$3 + 4^{2} - 2 \cdot 4$

Step 2.4

Raise $4$ to the power of $2$ .

$3 + 16 - 2 \cdot 4$

Step 2.5

Multiply $- 2$ by $4$ .

$3 + 16 - 8$

Step 2.6

Subtract $8$ from $16$ .

$3 + 8$

Step 2.7

Add $3$ and $8$ .

$11$

$11$

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