Solve 100/1.08+100/1.08^2+1100/1.08^3

$$\frac { 100 } { 1.08 } + \frac { 100 } { 1.08 ^ { 2 } } + \frac { 1100 } { 1.08 ^ { 3 } }$$

Evaluate

$$\frac{20697500}{19683}\approx 1051.541939745$$

Solution Steps

Expand \frac{100}{1.08} by multiplying both numerator and the denominator by 100.

$$\frac{10000}{108}+\frac{100}{1.08^{2}}+\frac{1100}{1.08^{3}}$$

Reduce the fraction \frac{10000}{108} to lowest terms by extracting and canceling out 4.

$$\frac{2500}{27}+\frac{100}{1.08^{2}}+\frac{1100}{1.08^{3}}$$

Calculate 1.08 to the power of 2 and get 1.1664.

$$\frac{2500}{27}+\frac{100}{1.1664}+\frac{1100}{1.08^{3}}$$

Expand \frac{100}{1.1664} by multiplying both numerator and the denominator by 10000.

$$\frac{2500}{27}+\frac{1000000}{11664}+\frac{1100}{1.08^{3}}$$

Reduce the fraction \frac{1000000}{11664} to lowest terms by extracting and canceling out 16.

$$\frac{2500}{27}+\frac{62500}{729}+\frac{1100}{1.08^{3}}$$

Least common multiple of 27 and 729 is 729. Convert \frac{2500}{27} and \frac{62500}{729} to fractions with denominator 729.

$$\frac{67500}{729}+\frac{62500}{729}+\frac{1100}{1.08^{3}}$$

Since \frac{67500}{729} and \frac{62500}{729} have the same denominator, add them by adding their numerators.

$$\frac{67500+62500}{729}+\frac{1100}{1.08^{3}}$$

Add 67500 and 62500 to get 130000.

$$\frac{130000}{729}+\frac{1100}{1.08^{3}}$$

Calculate 1.08 to the power of 3 and get 1.259712.

$$\frac{130000}{729}+\frac{1100}{1.259712}$$

Expand \frac{1100}{1.259712} by multiplying both numerator and the denominator by 1000000.

$$\frac{130000}{729}+\frac{1100000000}{1259712}$$

Reduce the fraction \frac{1100000000}{1259712} to lowest terms by extracting and canceling out 64.

$$\frac{130000}{729}+\frac{17187500}{19683}$$

Least common multiple of 729 and 19683 is 19683. Convert \frac{130000}{729} and \frac{17187500}{19683} to fractions with denominator 19683.

$$\frac{3510000}{19683}+\frac{17187500}{19683}$$

Since \frac{3510000}{19683} and \frac{17187500}{19683} have the same denominator, add them by adding their numerators.

$$\frac{3510000+17187500}{19683}$$

Add 3510000 and 17187500 to get 20697500.

$$\frac{20697500}{19683}$$

Factor

$$\frac{17 \cdot 487 \cdot 2 ^ {2} \cdot 5 ^ {4}}{3 ^ {9}} = 1051\frac{10667}{19683} = 1051.5419397449575$$