Calculus Examples

$\sum_{x = 3}^{4} \frac{- 21 x}{5}$

Step 1

Simplify the summation.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{21 x}{5}$

Step 1.2

Rewrite the summation.

$\sum_{x = 3}^{4} - \frac{21 x}{5}$

$\sum_{x = 3}^{4} - \frac{21 x}{5}$

Step 2

Expand the series for each value of $x$ .

$- \frac{21 \cdot 3}{5} - \frac{21 \cdot 4}{5}$

Step 3

Simplify.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{- 21 \cdot 3 - 21 \cdot 4}{5}$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $- 21$ by $3$ .

$\frac{- 63 - 21 \cdot 4}{5}$

Step 3.2.2

Multiply $- 21$ by $4$ .

$\frac{- 63 - 84}{5}$

$\frac{- 63 - 84}{5}$

Step 3.3

Subtract $84$ from $- 63$ .

$\frac{- 147}{5}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{147}{5}$

$- \frac{147}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{147}{5}$

Decimal Form:

$- 29.4$

Mixed Number Form:

$- 29 \frac{2}{5}$

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