Finite Math Examples

$s \cdot 25 = \frac{8 (1 - \frac{3}{4^{25}})}{1 - \frac{3}{4}}$

Step 1

Simplify.

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Step 1.1

Raise $4$ to the power of $25$ .

$s \cdot 25 = \frac{8 (1 - \frac{3}{1125899906842620})}{1 - \frac{3}{4}}$

Step 1.2

Cancel the common factor of $3$ and $1125899906842620$ .

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Step 1.2.1

Factor $3$ out of $3$ .

$s \cdot 25 = \frac{8 (1 - \frac{3 (1)}{1125899906842620})}{1 - \frac{3}{4}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $1125899906842620$ .

$s \cdot 25 = \frac{8 (1 - \frac{3 \cdot 1}{3 \cdot 375299968947540})}{1 - \frac{3}{4}}$

Step 1.2.2.2

Cancel the common factor.

$s \cdot 25 = \frac{8 (1 - \frac{3 \cdot 1}{3 \cdot 375299968947540})}{1 - \frac{3}{4}}$

Step 1.2.2.3

Rewrite the expression.

$s \cdot 25 = \frac{8 (1 - \frac{1}{375299968947540})}{1 - \frac{3}{4}}$

Step 1.3

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

$s \cdot 25 = \frac{8 (\frac{375299968947540}{375299968947540} - \frac{1}{375299968947540})}{1 - \frac{3}{4}}$

Step 1.4

Combine the numerators over the common denominator.

$s \cdot 25 = \frac{8 \frac{375299968947540 - 1}{375299968947540}}{1 - \frac{3}{4}}$

Step 1.5

Subtract $1$ from $375299968947540$ .

$s \cdot 25 = \frac{8 (\frac{375299968947539}{375299968947540})}{1 - \frac{3}{4}}$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Factor $4$ out of $8$ .

$s \cdot 25 = \frac{4 (2) \frac{375299968947539}{375299968947540}}{1 - \frac{3}{4}}$

Step 1.6.2

Factor $4$ out of $375299968947540$ .

$s \cdot 25 = \frac{4 \cdot 2 \frac{375299968947539}{4 \cdot 93824992236885}}{1 - \frac{3}{4}}$

Step 1.6.3

Cancel the common factor.

$s \cdot 25 = \frac{4 \cdot 2 \frac{375299968947539}{4 \cdot 93824992236885}}{1 - \frac{3}{4}}$

Step 1.6.4

Rewrite the expression.

$s \cdot 25 = \frac{2 (\frac{375299968947539}{93824992236885})}{1 - \frac{3}{4}}$

Step 1.7

Combine $2$ and $\frac{375299968947539}{93824992236885}$ .

$s \cdot 25 = \frac{\frac{2 \cdot 375299968947539}{93824992236885}}{1 - \frac{3}{4}}$

Step 1.8

Multiply $2$ by $375299968947539$ .

$s \cdot 25 = \frac{\frac{750599937895078}{93824992236885}}{1 - \frac{3}{4}}$

Step 1.9

Multiply the numerator by the reciprocal of the denominator.

$s \cdot 25 = \frac{750599937895078}{93824992236885} \cdot \frac{1}{1 - \frac{3}{4}}$

Step 1.10

Simplify the denominator.

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Step 1.10.1

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

$s \cdot 25 = \frac{750599937895078}{93824992236885} \cdot \frac{1}{\frac{4}{4} - \frac{3}{4}}$

Step 1.10.2

Combine the numerators over the common denominator.

$s \cdot 25 = \frac{750599937895078}{93824992236885} \cdot \frac{1}{\frac{4 - 3}{4}}$

Step 1.10.3

Subtract $3$ from $4$ .

$s \cdot 25 = \frac{750599937895078}{93824992236885} \cdot \frac{1}{\frac{1}{4}}$

Step 1.11

Multiply the numerator by the reciprocal of the denominator.

$s \cdot 25 = \frac{750599937895078}{93824992236885} (1 \cdot 4)$

Step 1.12

Multiply $4$ by $1$ .

$s \cdot 25 = \frac{750599937895078}{93824992236885} \cdot 4$

Step 1.13

Multiply $\frac{750599937895078}{93824992236885} \cdot 4$ .

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Step 1.13.1

Combine $\frac{750599937895078}{93824992236885}$ and $4$ .

$s \cdot 25 = \frac{750599937895078 \cdot 4}{93824992236885}$

Step 1.13.2

Multiply $750599937895078$ by $4$ .

$s \cdot 25 = \frac{3002399751580312}{93824992236885}$

Step 2

Divide each term in $s \cdot 25 = \frac{3002399751580312}{93824992236885}$ by $25$ and simplify.

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Step 2.1

Divide each term in $s \cdot 25 = \frac{3002399751580312}{93824992236885}$ by $25$ .

$\frac{s \cdot 25}{25} = \frac{\frac{3002399751580312}{93824992236885}}{25}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $25$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{s \cdot 25}{25} = \frac{\frac{3002399751580312}{93824992236885}}{25}$

Step 2.2.1.2

Divide $s$ by $1$ .

$s = \frac{\frac{3002399751580312}{93824992236885}}{25}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$s = \frac{3002399751580312}{93824992236885} \cdot \frac{1}{25}$

Step 2.3.2

Multiply $\frac{3002399751580312}{93824992236885} \cdot \frac{1}{25}$ .

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Step 2.3.2.1

Multiply $\frac{3002399751580312}{93824992236885}$ by $\frac{1}{25}$ .

$s = \frac{3002399751580312}{93824992236885 \cdot 25}$

Step 2.3.2.2

Multiply $93824992236885$ by $25$ .

$s = \frac{3002399751580312}{2345624805922125}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$s = \frac{3002399751580312}{2345624805922125}$

Decimal Form:

$s = 1.28$