Precalculus Examples

$\sum_{k = 4}^{5} k^{2} - k$

Step 1

Expand the series for each value of $k$ .

$4^{2} - 1 \cdot 4 + 5^{2} - 1 \cdot 5$

Step 2

Simplify.

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Step 2.1

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

$16 - 1 \cdot 4 + 5^{2} - 1 \cdot 5$

Step 2.2

Multiply $- 1$ by $4$ .

$16 - 4 + 5^{2} - 1 \cdot 5$

Step 2.3

Subtract $4$ from $16$ .

$12 + 5^{2} - 1 \cdot 5$

Step 2.4

Raise $5$ to the power of $2$ .

$12 + 25 - 1 \cdot 5$

Step 2.5

Multiply $- 1$ by $5$ .

$12 + 25 - 5$

Step 2.6

Subtract $5$ from $25$ .

$12 + 20$

Step 2.7

Add $12$ and $20$ .

$32$

$32$

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