Calculus Examples

$\sum_{k = 1}^{2} \frac{15 k}{k + 4}$

Step 1

Expand the series for each value of $k$ .

$\frac{15 \cdot 1}{1 + 4} + \frac{15 \cdot 2}{2 + 4}$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Multiply $15$ by $1$ .

$\frac{15}{1 + 4} + \frac{15 \cdot 2}{2 + 4}$

Step 2.2

Multiply $15$ by $2$ .

$\frac{15}{1 + 4} + \frac{30}{2 + 4}$

Step 2.3

Simplify each term.

Tap for more steps...

Step 2.3.1

Add $1$ and $4$ .

$\frac{15}{5} + \frac{30}{2 + 4}$

Step 2.3.2

Divide $15$ by $5$ .

$3 + \frac{30}{2 + 4}$

Step 2.3.3

Cancel the common factor of $30$ and $2 + 4$ .

Tap for more steps...

Step 2.3.3.1

Factor $2$ out of $30$ .

$3 + \frac{2 \cdot 15}{2 + 4}$

Step 2.3.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.3.2.1

Factor $2$ out of $2$ .

$3 + \frac{2 \cdot 15}{2 (1) + 4}$

Step 2.3.3.2.2

Factor $2$ out of $4$ .

$3 + \frac{2 \cdot 15}{2 \cdot 1 + 2 \cdot 2}$

Step 2.3.3.2.3

Factor $2$ out of $2 \cdot 1 + 2 \cdot 2$ .

$3 + \frac{2 \cdot 15}{2 \cdot (1 + 2)}$

Step 2.3.3.2.4

Cancel the common factor.

$3 + \frac{2 \cdot 15}{2 \cdot (1 + 2)}$

Step 2.3.3.2.5

Rewrite the expression.

$3 + \frac{15}{1 + 2}$

$3 + \frac{15}{1 + 2}$

$3 + \frac{15}{1 + 2}$

Step 2.3.4

Add $1$ and $2$ .

$3 + \frac{15}{3}$

Step 2.3.5

Divide $15$ by $3$ .

$3 + 5$

$3 + 5$

Step 2.4

Add $3$ and $5$ .

$8$

$8$

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