解決5000*((1+609%)^10-1/609%) |Microsoft數學求解器

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

評估

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

解題步驟

將 1 與 \frac{609}{100} 相加可以得到 \frac{709}{100}。

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

計算 \frac{709}{100} 的 10 乘冪，然後得到 \frac{32096845506516383920668257401}{100000000000000000000}。

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

從 \frac{32096845506516383920668257401}{100000000000000000000} 減去 1 會得到 \frac{32096845406516383920668257401}{100000000000000000000}。

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

\frac{32096845406516383920668257401}{100000000000000000000} 除以 \frac{609}{100} 的算法是將 \frac{32096845406516383920668257401}{100000000000000000000} 乘以 \frac{609}{100} 的倒數。

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

將 \frac{32096845406516383920668257401}{100000000000000000000} 乘上 \frac{100}{609} 得到 \frac{52704179649452190345924889}{1000000000000000000}。

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

將 5000 乘上 \frac{52704179649452190345924889}{1000000000000000000} 得到 \frac{52704179649452190345924889}{200000000000000}。

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

因式分解

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