Solve 450/1.17+550/1.17^2+650/1.17^3+750/1.17^4+frac{850}{1.17^5}

$$\frac { 450 } { 1.17 } + \frac { 550 } { 1.17 ^ { 2 } } + \frac { 650 } { 1.17 ^ { 3 } } + \frac { 750 } { 1.17 ^ { 4 } } + \frac { 850 } { 1.17 ^ { 5 } }$$

Evaluate

$$\frac{43414213945000}{21924480357}\approx 1980.170715022$$

Solution Steps

Expand \frac{450}{1.17} by multiplying both numerator and the denominator by 100.

$$\frac{45000}{117}+\frac{550}{1.17^{2}}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Reduce the fraction \frac{45000}{117} to lowest terms by extracting and canceling out 9.

$$\frac{5000}{13}+\frac{550}{1.17^{2}}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Calculate 1.17 to the power of 2 and get 1.3689.

$$\frac{5000}{13}+\frac{550}{1.3689}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Expand \frac{550}{1.3689} by multiplying both numerator and the denominator by 10000.

$$\frac{5000}{13}+\frac{5500000}{13689}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Least common multiple of 13 and 13689 is 13689. Convert \frac{5000}{13} and \frac{5500000}{13689} to fractions with denominator 13689.

$$\frac{5265000}{13689}+\frac{5500000}{13689}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Since \frac{5265000}{13689} and \frac{5500000}{13689} have the same denominator, add them by adding their numerators.

$$\frac{5265000+5500000}{13689}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Add 5265000 and 5500000 to get 10765000.

$$\frac{10765000}{13689}+\frac{650}{1.17^{3}}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Calculate 1.17 to the power of 3 and get 1.601613.

$$\frac{10765000}{13689}+\frac{650}{1.601613}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Expand \frac{650}{1.601613} by multiplying both numerator and the denominator by 1000000.

$$\frac{10765000}{13689}+\frac{650000000}{1601613}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Reduce the fraction \frac{650000000}{1601613} to lowest terms by extracting and canceling out 13.

$$\frac{10765000}{13689}+\frac{50000000}{123201}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Least common multiple of 13689 and 123201 is 123201. Convert \frac{10765000}{13689} and \frac{50000000}{123201} to fractions with denominator 123201.

$$\frac{96885000}{123201}+\frac{50000000}{123201}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Since \frac{96885000}{123201} and \frac{50000000}{123201} have the same denominator, add them by adding their numerators.

$$\frac{96885000+50000000}{123201}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Add 96885000 and 50000000 to get 146885000.

$$\frac{146885000}{123201}+\frac{750}{1.17^{4}}+\frac{850}{1.17^{5}}$$

Calculate 1.17 to the power of 4 and get 1.87388721.

$$\frac{146885000}{123201}+\frac{750}{1.87388721}+\frac{850}{1.17^{5}}$$

Expand \frac{750}{1.87388721} by multiplying both numerator and the denominator by 100000000.

$$\frac{146885000}{123201}+\frac{75000000000}{187388721}+\frac{850}{1.17^{5}}$$

Reduce the fraction \frac{75000000000}{187388721} to lowest terms by extracting and canceling out 3.

$$\frac{146885000}{123201}+\frac{25000000000}{62462907}+\frac{850}{1.17^{5}}$$

Least common multiple of 123201 and 62462907 is 62462907. Convert \frac{146885000}{123201} and \frac{25000000000}{62462907} to fractions with denominator 62462907.

$$\frac{74470695000}{62462907}+\frac{25000000000}{62462907}+\frac{850}{1.17^{5}}$$

Since \frac{74470695000}{62462907} and \frac{25000000000}{62462907} have the same denominator, add them by adding their numerators.

$$\frac{74470695000+25000000000}{62462907}+\frac{850}{1.17^{5}}$$

Add 74470695000 and 25000000000 to get 99470695000.

$$\frac{99470695000}{62462907}+\frac{850}{1.17^{5}}$$

Calculate 1.17 to the power of 5 and get 2.1924480357.

$$\frac{99470695000}{62462907}+\frac{850}{2.1924480357}$$

Expand \frac{850}{2.1924480357} by multiplying both numerator and the denominator by 10000000000.

$$\frac{99470695000}{62462907}+\frac{8500000000000}{21924480357}$$

Least common multiple of 62462907 and 21924480357 is 21924480357. Convert \frac{99470695000}{62462907} and \frac{8500000000000}{21924480357} to fractions with denominator 21924480357.

$$\frac{34914213945000}{21924480357}+\frac{8500000000000}{21924480357}$$

Since \frac{34914213945000}{21924480357} and \frac{8500000000000}{21924480357} have the same denominator, add them by adding their numerators.

$$\frac{34914213945000+8500000000000}{21924480357}$$

Add 34914213945000 and 8500000000000 to get 43414213945000.

$$\frac{43414213945000}{21924480357}$$

Factor

$$\frac{8682842789 \cdot 2 ^ {3} \cdot 5 ^ {4}}{3 ^ {10} \cdot 13 ^ {5}} = 1980\frac{3742838140}{21924480357} = 1980.1707150217042$$