Solve 1200/1-(frac{1{106})^20}

$$\frac { 1200 } { 1 - ( \frac { 1 } { 106 } ) ^ { 20 } }$$

Evaluate

$$\frac{513141675554055157101278877532471863279616}{427618062961712630917732397943726552733}\approx 1200$$

Solution Steps

Calculate \frac{1}{106} to the power of 20 and get \frac{1}{32071354722128447318829929845779491454976}.

$$\frac{1200}{1-\frac{1}{32071354722128447318829929845779491454976}}$$

Convert 1 to fraction \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454976}.

$$\frac{1200}{\frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454976}-\frac{1}{32071354722128447318829929845779491454976}}$$

Since \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454976} and \frac{1}{32071354722128447318829929845779491454976} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1200}{\frac{32071354722128447318829929845779491454976-1}{32071354722128447318829929845779491454976}}$$

Subtract 1 from 32071354722128447318829929845779491454976 to get 32071354722128447318829929845779491454975.

$$\frac{1200}{\frac{32071354722128447318829929845779491454975}{32071354722128447318829929845779491454976}}$$

Divide 1200 by \frac{32071354722128447318829929845779491454975}{32071354722128447318829929845779491454976} by multiplying 1200 by the reciprocal of \frac{32071354722128447318829929845779491454975}{32071354722128447318829929845779491454976}.

$$1200\times \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454975}$$

Express 1200\times \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454975} as a single fraction.

$$\frac{1200\times 32071354722128447318829929845779491454976}{32071354722128447318829929845779491454975}$$

Multiply 1200 and 32071354722128447318829929845779491454976 to get 38485625666554136782595915814935389745971200.

$$\frac{38485625666554136782595915814935389745971200}{32071354722128447318829929845779491454975}$$

Reduce the fraction \frac{38485625666554136782595915814935389745971200}{32071354722128447318829929845779491454975} to lowest terms by extracting and canceling out 75.

$$\frac{513141675554055157101278877532471863279616}{427618062961712630917732397943726552733}$$

Factor

$$\frac{2 ^ {24} \cdot 53 ^ {20}}{7 \cdot 11 \cdot 17 \cdot 107 \cdot 241 \cdot 571 \cdot 661 \cdot 2251 \cdot 5051 \cdot 44641 \cdot 1957121 \cdot 33788861} = 1199\frac{4.2761806296165705 \times 10^{38}}{4.2761806296171265 \times 10^{38}} = 1199.9999999999998$$