Calculus Examples

${(1 + \frac{1}{1000})}^{3}$

Step 1

Write $1$ as a fraction with a common denominator.

${(\frac{1000}{1000} + \frac{1}{1000})}^{3}$

Step 2

Combine the numerators over the common denominator.

${(\frac{1000 + 1}{1000})}^{3}$

Step 3

Add $1000$ and $1$ .

${(\frac{1001}{1000})}^{3}$

Step 4

Apply the product rule to $\frac{1001}{1000}$ .

$\frac{1001^{3}}{1000^{3}}$

Step 5

Raise $1001$ to the power of $3$ .

$\frac{1003003001}{1000^{3}}$

Step 6

Raise $1000$ to the power of $3$ .

$\frac{1003003001}{1000000000}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1003003001}{1000000000}$

Decimal Form:

$1.\overline{003}$

Mixed Number Form:

$1 \frac{3003001}{1000000000}$