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

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

I-evaluate

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

Mga Hakbang ng Solution

Kalkulahin ang \frac{1}{106} sa power ng 20 at kunin ang \frac{1}{32071354722128447318829929845779491454976}.

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

I-convert ang 1 sa fraction na \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454976}.

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

Dahil may parehong denominator ang \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454976} at \frac{1}{32071354722128447318829929845779491454976}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

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

I-subtract ang 1 mula sa 32071354722128447318829929845779491454976 para makuha ang 32071354722128447318829929845779491454975.

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

I-divide ang 1200 gamit ang \frac{32071354722128447318829929845779491454975}{32071354722128447318829929845779491454976} sa pamamagitan ng pagmu-multiply sa 1200 gamit ang reciprocal ng \frac{32071354722128447318829929845779491454975}{32071354722128447318829929845779491454976}.

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

Ipakita ang 1200\times \frac{32071354722128447318829929845779491454976}{32071354722128447318829929845779491454975} bilang isang single fraction.

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

I-multiply ang 1200 at 32071354722128447318829929845779491454976 para makuha ang 38485625666554136782595915814935389745971200.

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

Bawasan ang fraction \frac{38485625666554136782595915814935389745971200}{32071354722128447318829929845779491454975} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 75.

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

I-factor

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