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Precalculus Examples

$\sum_{x = 2}^{3} \frac{7}{2} x$

Step 1

Simplify the summation.

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Step 1.1

Combine

$\frac{7}{2}$ and

$x$ .

$\frac{7 x}{2}$

Step 1.2

Rewrite the summation.

$\sum_{x = 2}^{3} \frac{7 x}{2}$

$\sum_{x = 2}^{3} \frac{7 x}{2}$

Step 2

Expand the series for each value of

$x$ .

$\frac{7 \cdot 2}{2} + \frac{7 \cdot 3}{2}$

Step 3

Simplify.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 7 \cdot 3}{2}$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply

$7$ by

$2$ .

$\frac{14 + 7 \cdot 3}{2}$

Step 3.2.2

Multiply

$7$ by

$3$ .

$\frac{14 + 21}{2}$

$\frac{14 + 21}{2}$

Step 3.3

Add

$14$ and

$21$ .

$\frac{35}{2}$

$\frac{35}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{2}$

Decimal Form:

$17.5$

Mixed Number Form:

$17 \frac{1}{2}$

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