Решете 5000*((1+609%)^10-1/609%)

$$5000 \times ( \frac { ( 1 + 609 \% ) ^ { 10 } - 1 } { 609 \% } )$$

Изчисляване

$$\frac{52704179649452190345924889}{200000000000000}\approx 263520898247,26095173$$

Стъпки на решението

Съберете 1 и \frac{609}{100}, за да се получи \frac{709}{100}.

$$5000\times \frac{\left(\frac{709}{100}\right)^{10}-1}{\frac{609}{100}}$$

Изчислявате 10 на степен \frac{709}{100} и получавате \frac{32096845506516383920668257401}{100000000000000000000}.

$$5000\times \frac{\frac{32096845506516383920668257401}{100000000000000000000}-1}{\frac{609}{100}}$$

Извадете 1 от \frac{32096845506516383920668257401}{100000000000000000000}, за да получите \frac{32096845406516383920668257401}{100000000000000000000}.

$$5000\times \frac{\frac{32096845406516383920668257401}{100000000000000000000}}{\frac{609}{100}}$$

Разделете \frac{32096845406516383920668257401}{100000000000000000000} на \frac{609}{100} чрез умножаване на \frac{32096845406516383920668257401}{100000000000000000000} по обратната стойност на \frac{609}{100}.

$$5000\times \frac{32096845406516383920668257401}{100000000000000000000}\times \frac{100}{609}$$

Умножете \frac{32096845406516383920668257401}{100000000000000000000} по \frac{100}{609}, за да получите \frac{52704179649452190345924889}{1000000000000000000}.

$$5000\times \frac{52704179649452190345924889}{1000000000000000000}$$

Умножете 5000 по \frac{52704179649452190345924889}{1000000000000000000}, за да получите \frac{52704179649452190345924889}{200000000000000}.

$$\frac{52704179649452190345924889}{200000000000000}$$

Разлагане на множители

$$\frac{11 \cdot 311 \cdot 401 \cdot 809 \cdot 66688751 \cdot 712109051}{2 ^ {15} \cdot 5 ^ {14}} = 263520898247\frac{52196937859072}{200000000000000} = 263520898247,261$$