Ratkaise 5000*((1+609%)^10-1/609%)

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

Laske

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

Ratkaisun vaiheet

Selvitä \frac{709}{100} laskemalla yhteen 1 ja \frac{609}{100}.

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

Laske \frac{709}{100} potenssiin 10, jolloin ratkaisuksi tulee \frac{32096845506516383920668257401}{100000000000000000000}.

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

Vähennä 1 luvusta \frac{32096845506516383920668257401}{100000000000000000000} saadaksesi tuloksen \frac{32096845406516383920668257401}{100000000000000000000}.

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

Jaa \frac{32096845406516383920668257401}{100000000000000000000} luvulla \frac{609}{100} kertomalla \frac{32096845406516383920668257401}{100000000000000000000} luvun \frac{609}{100} käänteisluvulla.

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

Kerro \frac{32096845406516383920668257401}{100000000000000000000} ja \frac{100}{609}, niin saadaan \frac{52704179649452190345924889}{1000000000000000000}.

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

Kerro 5000 ja \frac{52704179649452190345924889}{1000000000000000000}, niin saadaan \frac{52704179649452190345924889}{200000000000000}.

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

Jaa tekijöihin

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