求解 5000*((1+609%)^10-1/609%)

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

求值

$$\frac{52704179649452190345924889}{200000000000000}\approx 263520898247.26095173$$

求解步骤

1 与 \frac{609}{100} 相加，得到 \frac{709}{100}。

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

计算 10 的 \frac{709}{100} 乘方，得到 \frac{32096845506516383920668257401}{100000000000000000000}。

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

将 \frac{32096845506516383920668257401}{100000000000000000000} 减去 1，得到 \frac{32096845406516383920668257401}{100000000000000000000}。

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

\frac{32096845406516383920668257401}{100000000000000000000} 除以 \frac{609}{100} 的计算方法是用 \frac{32096845406516383920668257401}{100000000000000000000} 乘以 \frac{609}{100} 的倒数。

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

将 \frac{32096845406516383920668257401}{100000000000000000000} 与 \frac{100}{609} 相乘，得到 \frac{52704179649452190345924889}{1000000000000000000}。

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

将 5000 与 \frac{52704179649452190345924889}{1000000000000000000} 相乘，得到 \frac{52704179649452190345924889}{200000000000000}。

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

因式分解

$$\frac{11 \cdot 311 \cdot 401 \cdot 809 \cdot 66688751 \cdot 712109051}{2 ^ {15} \cdot 5 ^ {14}} = 263520898247\frac{52196937859072}{200000000000000} = 263520898247.261$$