Solve 30000*1.1^10*0.1/1.1^10-1

$$30000 \times 1.1 ^ { 10 } \times \frac { 0.1 } { 1.1 ^ { 10 } - 1 }$$

Evaluate

$$\frac{25937424601000}{5312474867}\approx 4882.361846475$$

Solution Steps

Calculate 1.1 to the power of 10 and get 2.5937424601.

$$30000\times 2.5937424601\times \frac{0.1}{1.1^{10}-1}$$

Multiply 30000 and 2.5937424601 to get 77812.273803.

$$77812.273803\times \frac{0.1}{1.1^{10}-1}$$

Calculate 1.1 to the power of 10 and get 2.5937424601.

$$77812.273803\times \frac{0.1}{2.5937424601-1}$$

Subtract 1 from 2.5937424601 to get 1.5937424601.

$$77812.273803\times \frac{0.1}{1.5937424601}$$

Expand \frac{0.1}{1.5937424601} by multiplying both numerator and the denominator by 10000000000.

$$77812.273803\times \frac{1000000000}{15937424601}$$

Convert decimal number 77812.273803 to fraction \frac{77812273803}{1000000}.

$$\frac{77812273803}{1000000}\times \frac{1000000000}{15937424601}$$

Multiply \frac{77812273803}{1000000} times \frac{1000000000}{15937424601} by multiplying numerator times numerator and denominator times denominator.

$$\frac{77812273803\times 1000000000}{1000000\times 15937424601}$$

Do the multiplications in the fraction \frac{77812273803\times 1000000000}{1000000\times 15937424601}.

$$\frac{77812273803000000000}{15937424601000000}$$

Reduce the fraction \frac{77812273803000000000}{15937424601000000} to lowest terms by extracting and canceling out 3000000.

$$\frac{25937424601000}{5312474867}$$

Factor

$$\frac{2 ^ {3} \cdot 5 ^ {3} \cdot 11 ^ {10}}{7 \cdot 31 \cdot 401 \cdot 61051} = 4882\frac{1922300306}{5312474867} = 4882.361846475348$$