Calculus Examples

$\sum_{i = 2}^{5} \frac{300}{i}$

Step 1

Expand the series for each value of $i$ .

$\frac{300}{2} + \frac{300}{3} + \frac{300}{4} + \frac{300}{5}$

Step 2

Simplify.

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Step 2.1

Find the common denominator.

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Step 2.1.1

Multiply $\frac{300}{2}$ by $\frac{30}{30}$ .

$\frac{300}{2} \cdot \frac{30}{30} + \frac{300}{3} + \frac{300}{4} + \frac{300}{5}$

Step 2.1.2

Multiply $\frac{300}{2}$ by $\frac{30}{30}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300}{3} + \frac{300}{4} + \frac{300}{5}$

Step 2.1.3

Multiply $\frac{300}{3}$ by $\frac{20}{20}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300}{3} \cdot \frac{20}{20} + \frac{300}{4} + \frac{300}{5}$

Step 2.1.4

Multiply $\frac{300}{3}$ by $\frac{20}{20}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300 \cdot 20}{3 \cdot 20} + \frac{300}{4} + \frac{300}{5}$

Step 2.1.5

Multiply $\frac{300}{4}$ by $\frac{15}{15}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300 \cdot 20}{3 \cdot 20} + \frac{300}{4} \cdot \frac{15}{15} + \frac{300}{5}$

Step 2.1.6

Multiply $\frac{300}{4}$ by $\frac{15}{15}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300 \cdot 20}{3 \cdot 20} + \frac{300 \cdot 15}{4 \cdot 15} + \frac{300}{5}$

Step 2.1.7

Multiply $\frac{300}{5}$ by $\frac{12}{12}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300 \cdot 20}{3 \cdot 20} + \frac{300 \cdot 15}{4 \cdot 15} + \frac{300}{5} \cdot \frac{12}{12}$

Step 2.1.8

Multiply $\frac{300}{5}$ by $\frac{12}{12}$ .

$\frac{300 \cdot 30}{2 \cdot 30} + \frac{300 \cdot 20}{3 \cdot 20} + \frac{300 \cdot 15}{4 \cdot 15} + \frac{300 \cdot 12}{5 \cdot 12}$

Step 2.1.9

Multiply $2$ by $30$ .

$\frac{300 \cdot 30}{60} + \frac{300 \cdot 20}{3 \cdot 20} + \frac{300 \cdot 15}{4 \cdot 15} + \frac{300 \cdot 12}{5 \cdot 12}$

Step 2.1.10

Multiply $3$ by $20$ .

$\frac{300 \cdot 30}{60} + \frac{300 \cdot 20}{60} + \frac{300 \cdot 15}{4 \cdot 15} + \frac{300 \cdot 12}{5 \cdot 12}$

Step 2.1.11

Multiply $4$ by $15$ .

$\frac{300 \cdot 30}{60} + \frac{300 \cdot 20}{60} + \frac{300 \cdot 15}{60} + \frac{300 \cdot 12}{5 \cdot 12}$

Step 2.1.12

Multiply $5$ by $12$ .

$\frac{300 \cdot 30}{60} + \frac{300 \cdot 20}{60} + \frac{300 \cdot 15}{60} + \frac{300 \cdot 12}{60}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{300 \cdot 30 + 300 \cdot 20 + 300 \cdot 15 + 300 \cdot 12}{60}$

Step 2.3

Simplify each term.

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Step 2.3.1

Multiply $300$ by $30$ .

$\frac{9000 + 300 \cdot 20 + 300 \cdot 15 + 300 \cdot 12}{60}$

Step 2.3.2

Multiply $300$ by $20$ .

$\frac{9000 + 6000 + 300 \cdot 15 + 300 \cdot 12}{60}$

Step 2.3.3

Multiply $300$ by $15$ .

$\frac{9000 + 6000 + 4500 + 300 \cdot 12}{60}$

Step 2.3.4

Multiply $300$ by $12$ .

$\frac{9000 + 6000 + 4500 + 3600}{60}$

Step 2.4

Add $9000$ and $6000$ .

$\frac{15000 + 4500 + 3600}{60}$

Step 2.5

Add $15000$ and $4500$ .

$\frac{19500 + 3600}{60}$

Step 2.6

Add $19500$ and $3600$ .

$\frac{23100}{60}$

Step 2.7

Divide $23100$ by $60$ .

$385$