Solve 6/1,02+6/1,03^2+6/1,038^3+106/1,044^2

$$\frac { 6 } { 1,02 } + \frac { 6 } { 1,03 ^ { 2 } } + \frac { 6 } { 1,038 ^ { 3 } } + \frac { 106 } { 1,044 ^ { 2 } }$$

Evaluate

$$\frac{2236173911}{338615112}\approx 6,603881019$$

Solution Steps

Expand \frac{6}{1,02} by multiplying both numerator and the denominator by 100.

$$\frac{600}{102}+\frac{6}{1\times 3^{2}}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Reduce the fraction \frac{600}{102} to lowest terms by extracting and canceling out 6.

$$\frac{100}{17}+\frac{6}{1\times 3^{2}}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{100}{17}+\frac{6}{1\times 9}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Multiply 1 and 9 to get 9.

$$\frac{100}{17}+\frac{6}{9}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{100}{17}+\frac{2}{3}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Least common multiple of 17 and 3 is 51. Convert \frac{100}{17} and \frac{2}{3} to fractions with denominator 51.

$$\frac{300}{51}+\frac{34}{51}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Since \frac{300}{51} and \frac{34}{51} have the same denominator, add them by adding their numerators.

$$\frac{300+34}{51}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Add 300 and 34 to get 334.

$$\frac{334}{51}+\frac{6}{1\times 38^{3}}+\frac{106}{1\times 44^{2}}$$

Calculate 38 to the power of 3 and get 54872.

$$\frac{334}{51}+\frac{6}{1\times 54872}+\frac{106}{1\times 44^{2}}$$

Multiply 1 and 54872 to get 54872.

$$\frac{334}{51}+\frac{6}{54872}+\frac{106}{1\times 44^{2}}$$

Reduce the fraction \frac{6}{54872} to lowest terms by extracting and canceling out 2.

$$\frac{334}{51}+\frac{3}{27436}+\frac{106}{1\times 44^{2}}$$

Least common multiple of 51 and 27436 is 1399236. Convert \frac{334}{51} and \frac{3}{27436} to fractions with denominator 1399236.

$$\frac{9163624}{1399236}+\frac{153}{1399236}+\frac{106}{1\times 44^{2}}$$

Since \frac{9163624}{1399236} and \frac{153}{1399236} have the same denominator, add them by adding their numerators.

$$\frac{9163624+153}{1399236}+\frac{106}{1\times 44^{2}}$$

Add 9163624 and 153 to get 9163777.

$$\frac{9163777}{1399236}+\frac{106}{1\times 44^{2}}$$

Calculate 44 to the power of 2 and get 1936.

$$\frac{9163777}{1399236}+\frac{106}{1\times 1936}$$

Multiply 1 and 1936 to get 1936.

$$\frac{9163777}{1399236}+\frac{106}{1936}$$

Reduce the fraction \frac{106}{1936} to lowest terms by extracting and canceling out 2.

$$\frac{9163777}{1399236}+\frac{53}{968}$$

Least common multiple of 1399236 and 968 is 338615112. Convert \frac{9163777}{1399236} and \frac{53}{968} to fractions with denominator 338615112.

$$\frac{2217634034}{338615112}+\frac{18539877}{338615112}$$

Since \frac{2217634034}{338615112} and \frac{18539877}{338615112} have the same denominator, add them by adding their numerators.

$$\frac{2217634034+18539877}{338615112}$$

Add 2217634034 and 18539877 to get 2236173911.

$$\frac{2236173911}{338615112}$$

Factor

$$\frac{3727 \cdot 599993}{3 \cdot 17 \cdot 2 ^ {3} \cdot 11 ^ {2} \cdot 19 ^ {3}} = 6\frac{204483239}{338615112} = 6.603881019344464$$