Calculus Examples

$\sum_{i = 1}^{4} \frac{7 i}{4 n - 9}$

Step 1

Expand the series for each value of $i$ .

$\frac{7 \cdot 1}{4 n - 9} + \frac{7 \cdot 2}{4 n - 9} + \frac{7 \cdot 3}{4 n - 9} + \frac{7 \cdot 4}{4 n - 9}$

Step 2

Simplify.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{7 \cdot 1 + 7 \cdot 2 + 7 \cdot 3 + 7 \cdot 4}{4 n - 9}$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $7$ by $1$ .

$\frac{7 + 7 \cdot 2 + 7 \cdot 3 + 7 \cdot 4}{4 n - 9}$

Step 2.2.2

Multiply $7$ by $2$ .

$\frac{7 + 14 + 7 \cdot 3 + 7 \cdot 4}{4 n - 9}$

Step 2.2.3

Multiply $7$ by $3$ .

$\frac{7 + 14 + 21 + 7 \cdot 4}{4 n - 9}$

Step 2.2.4

Multiply $7$ by $4$ .

$\frac{7 + 14 + 21 + 28}{4 n - 9}$

Step 2.3

Add $7$ and $14$ .

$\frac{21 + 21 + 28}{4 n - 9}$

Step 2.4

Add $21$ and $21$ .

$\frac{42 + 28}{4 n - 9}$

Step 2.5

Add $42$ and $28$ .

$\frac{70}{4 n - 9}$