Precalculus Examples

$\sum_{x = 4}^{8} 5 x^{2} + 5 x - 5 \sum_{x = 4}^{8} x^{2}$

Step 1

Evaluate $\sum_{x = 4}^{8} 5 x^{2} + 5 x$ .

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Step 1.1

Expand the series for each value of $x$ .

$5 \cdot 4^{2} + 5 \cdot 4 + 5 \cdot 5^{2} + 5 \cdot 5 + 5 \cdot 6^{2} + 5 \cdot 6 + \dots + 5 \cdot 8^{2} + 5 \cdot 8$

Step 1.2

Simplify the expanded form.

$1100$

Step 2

Evaluate $- 5 \sum_{x = 4}^{8} x^{2}$ .

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Step 2.1

Expand the series for each value of $x$ .

$- 5 (4^{2} + 5^{2} + 6^{2} + \dots + 8^{2})$

Step 2.2

Simplify the expanded form.

$- 950$

Step 3

Subtract $950$ from $1100$ .

$150$