Solve 10+10/1.046035+10/(1.046035)^2+10/(1.046035)^3=

$$10 + \frac { 10 } { 1.046035 } + \frac { 10 } { ( 1.046035 ) ^ { 2 } } + \frac { 10 } { ( 1.046035 ) ^ { 3 } } =$$

Evaluate

$$\frac{342782755459927430}{9156481776192743}\approx 37.436076851$$

Solution Steps

Expand \frac{10}{1.046035} by multiplying both numerator and the denominator by 1000000.

$$10+\frac{10000000}{1046035}+\frac{10}{1.046035^{2}}+\frac{10}{1.046035^{3}}$$

Reduce the fraction \frac{10000000}{1046035} to lowest terms by extracting and canceling out 5.

$$10+\frac{2000000}{209207}+\frac{10}{1.046035^{2}}+\frac{10}{1.046035^{3}}$$

Convert 10 to fraction \frac{2092070}{209207}.

$$\frac{2092070}{209207}+\frac{2000000}{209207}+\frac{10}{1.046035^{2}}+\frac{10}{1.046035^{3}}$$

Since \frac{2092070}{209207} and \frac{2000000}{209207} have the same denominator, add them by adding their numerators.

$$\frac{2092070+2000000}{209207}+\frac{10}{1.046035^{2}}+\frac{10}{1.046035^{3}}$$

Add 2092070 and 2000000 to get 4092070.

$$\frac{4092070}{209207}+\frac{10}{1.046035^{2}}+\frac{10}{1.046035^{3}}$$

Calculate 1.046035 to the power of 2 and get 1.094189221225.

$$\frac{4092070}{209207}+\frac{10}{1.094189221225}+\frac{10}{1.046035^{3}}$$

Expand \frac{10}{1.094189221225} by multiplying both numerator and the denominator by 1000000000000.

$$\frac{4092070}{209207}+\frac{10000000000000}{1094189221225}+\frac{10}{1.046035^{3}}$$

Reduce the fraction \frac{10000000000000}{1094189221225} to lowest terms by extracting and canceling out 25.

$$\frac{4092070}{209207}+\frac{400000000000}{43767568849}+\frac{10}{1.046035^{3}}$$

Least common multiple of 209207 and 43767568849 is 43767568849. Convert \frac{4092070}{209207} and \frac{400000000000}{43767568849} to fractions with denominator 43767568849.

$$\frac{856089688490}{43767568849}+\frac{400000000000}{43767568849}+\frac{10}{1.046035^{3}}$$

Since \frac{856089688490}{43767568849} and \frac{400000000000}{43767568849} have the same denominator, add them by adding their numerators.

$$\frac{856089688490+400000000000}{43767568849}+\frac{10}{1.046035^{3}}$$

Add 856089688490 and 400000000000 to get 1256089688490.

$$\frac{1256089688490}{43767568849}+\frac{10}{1.046035^{3}}$$

Calculate 1.046035 to the power of 3 and get 1.144560222024092875.

$$\frac{1256089688490}{43767568849}+\frac{10}{1.144560222024092875}$$

Expand \frac{10}{1.144560222024092875} by multiplying both numerator and the denominator by 1000000000000000000.

$$\frac{1256089688490}{43767568849}+\frac{10000000000000000000}{1144560222024092875}$$

Reduce the fraction \frac{10000000000000000000}{1144560222024092875} to lowest terms by extracting and canceling out 125.

$$\frac{1256089688490}{43767568849}+\frac{80000000000000000}{9156481776192743}$$

Least common multiple of 43767568849 and 9156481776192743 is 9156481776192743. Convert \frac{1256089688490}{43767568849} and \frac{80000000000000000}{9156481776192743} to fractions with denominator 9156481776192743.

$$\frac{262782755459927430}{9156481776192743}+\frac{80000000000000000}{9156481776192743}$$

Since \frac{262782755459927430}{9156481776192743} and \frac{80000000000000000}{9156481776192743} have the same denominator, add them by adding their numerators.

$$\frac{262782755459927430+80000000000000000}{9156481776192743}$$

Add 262782755459927430 and 80000000000000000 to get 342782755459927430.

$$\frac{342782755459927430}{9156481776192743}$$

Factor

$$\frac{2 \cdot 5 \cdot 17 \cdot 24071 \cdot 83767568849}{131 ^ {3} \cdot 1597 ^ {3}} = 37\frac{3992929740795896}{9156481776192744} = 37.43607685117418$$