Solve for s4 s_4=(1(1-(1/7)^4))/(1-1/7)

$s_{4} = \frac{1 (1 - {(\frac{1}{7})}^{4})}{1 - \frac{1}{7}}$

Step 1

Multiply $1 - {(\frac{1}{7})}^{4}$ by $1$ .

$s_{4} = \frac{1 - {(\frac{1}{7})}^{4}}{1 - \frac{1}{7}}$

Step 2

Simplify the denominator.

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

$s_{4} = \frac{1 - {(\frac{1}{7})}^{4}}{\frac{7}{7} - \frac{1}{7}}$

Combine the numerators over the common denominator.

$s_{4} = \frac{1 - {(\frac{1}{7})}^{4}}{\frac{7 - 1}{7}}$

Subtract $1$ from $7$ .

$s_{4} = \frac{1 - {(\frac{1}{7})}^{4}}{\frac{6}{7}}$

Step 3

Simplify the numerator.

Apply the product rule to $\frac{1}{7}$ .

$s_{4} = \frac{1 - \frac{1^{4}}{7^{4}}}{\frac{6}{7}}$

One to any power is one.

$s_{4} = \frac{1 - \frac{1}{7^{4}}}{\frac{6}{7}}$

Raise $7$ to the power of $4$ .

$s_{4} = \frac{1 - \frac{1}{2401}}{\frac{6}{7}}$

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

$s_{4} = \frac{\frac{2401}{2401} - \frac{1}{2401}}{\frac{6}{7}}$

Combine the numerators over the common denominator.

$s_{4} = \frac{\frac{2401 - 1}{2401}}{\frac{6}{7}}$

Subtract $1$ from $2401$ .

$s_{4} = \frac{\frac{2400}{2401}}{\frac{6}{7}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$s_{4} = \frac{2400}{2401} \cdot \frac{7}{6}$

Step 5

Cancel the common factor of $6$ .

Factor $6$ out of $2400$ .

$s_{4} = \frac{6 (400)}{2401} \cdot \frac{7}{6}$

Cancel the common factor.

$s_{4} = \frac{6 \cdot 400}{2401} \cdot \frac{7}{6}$

Rewrite the expression.

$s_{4} = \frac{400}{2401} \cdot 7$

Step 6

Cancel the common factor of $7$ .

Factor $7$ out of $2401$ .

$s_{4} = \frac{400}{7 (343)} \cdot 7$

Cancel the common factor.

$s_{4} = \frac{400}{7 \cdot 343} \cdot 7$

Rewrite the expression.

$s_{4} = \frac{400}{343}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s_{4} = \frac{400}{343}$

Decimal Form:

$s_{4} = 1.16618075 \dots$

Mixed Number Form:

$s_{4} = 1 \frac{57}{343}$

Solve for s4 s_4=(1(1-(1/7)^4))/(1-1/7)

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