Calculus Examples

$\sum_{k = 1}^{2} \frac{72 k}{k + 7}$

Step 1

Expand the series for each value of $k$ .

$\frac{72 \cdot 1}{1 + 7} + \frac{72 \cdot 2}{2 + 7}$

Step 2

Simplify.

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Step 2.1

Multiply $72$ by $1$ .

$\frac{72}{1 + 7} + \frac{72 \cdot 2}{2 + 7}$

Step 2.2

Multiply $72$ by $2$ .

$\frac{72}{1 + 7} + \frac{144}{2 + 7}$

Step 2.3

Simplify each term.

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Step 2.3.1

Add $1$ and $7$ .

$\frac{72}{8} + \frac{144}{2 + 7}$

Step 2.3.2

Divide $72$ by $8$ .

$9 + \frac{144}{2 + 7}$

Step 2.3.3

Add $2$ and $7$ .

$9 + \frac{144}{9}$

Step 2.3.4

Divide $144$ by $9$ .

$9 + 16$

Step 2.4

Add $9$ and $16$ .

$25$