Solve 40000/1.18+60000/1.18^2+70000/1.18^3+60000/1.18^4+frac{40000}{1.18^5}=

$$\frac{ 40000 }{ 1.18 } + \frac{ 60000 }{ { 1.18 }^{ 2 } } + \frac{ 70000 }{ { 1.18 }^{ 3 } } + \frac{ 60000 }{ { 1.18 }^{ 4 } } + \frac{ 40000 }{ { 1.18 }^{ 5 } } =$$

Evaluate

$$\frac{120125322000000}{714924299}\approx 168025.233116325$$

Solution Steps

Expand \frac{40000}{1.18} by multiplying both numerator and the denominator by 100.

$$\frac{4000000}{118}+\frac{60000}{1.18^{2}}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Reduce the fraction \frac{4000000}{118} to lowest terms by extracting and canceling out 2.

$$\frac{2000000}{59}+\frac{60000}{1.18^{2}}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Calculate 1.18 to the power of 2 and get 1.3924.

$$\frac{2000000}{59}+\frac{60000}{1.3924}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Expand \frac{60000}{1.3924} by multiplying both numerator and the denominator by 10000.

$$\frac{2000000}{59}+\frac{600000000}{13924}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Reduce the fraction \frac{600000000}{13924} to lowest terms by extracting and canceling out 4.

$$\frac{2000000}{59}+\frac{150000000}{3481}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Least common multiple of 59 and 3481 is 3481. Convert \frac{2000000}{59} and \frac{150000000}{3481} to fractions with denominator 3481.

$$\frac{118000000}{3481}+\frac{150000000}{3481}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Since \frac{118000000}{3481} and \frac{150000000}{3481} have the same denominator, add them by adding their numerators.

$$\frac{118000000+150000000}{3481}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Add 118000000 and 150000000 to get 268000000.

$$\frac{268000000}{3481}+\frac{70000}{1.18^{3}}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Calculate 1.18 to the power of 3 and get 1.643032.

$$\frac{268000000}{3481}+\frac{70000}{1.643032}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Expand \frac{70000}{1.643032} by multiplying both numerator and the denominator by 1000000.

$$\frac{268000000}{3481}+\frac{70000000000}{1643032}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Reduce the fraction \frac{70000000000}{1643032} to lowest terms by extracting and canceling out 8.

$$\frac{268000000}{3481}+\frac{8750000000}{205379}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Least common multiple of 3481 and 205379 is 205379. Convert \frac{268000000}{3481} and \frac{8750000000}{205379} to fractions with denominator 205379.

$$\frac{15812000000}{205379}+\frac{8750000000}{205379}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Since \frac{15812000000}{205379} and \frac{8750000000}{205379} have the same denominator, add them by adding their numerators.

$$\frac{15812000000+8750000000}{205379}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Add 15812000000 and 8750000000 to get 24562000000.

$$\frac{24562000000}{205379}+\frac{60000}{1.18^{4}}+\frac{40000}{1.18^{5}}$$

Calculate 1.18 to the power of 4 and get 1.93877776.

$$\frac{24562000000}{205379}+\frac{60000}{1.93877776}+\frac{40000}{1.18^{5}}$$

Expand \frac{60000}{1.93877776} by multiplying both numerator and the denominator by 100000000.

$$\frac{24562000000}{205379}+\frac{6000000000000}{193877776}+\frac{40000}{1.18^{5}}$$

Reduce the fraction \frac{6000000000000}{193877776} to lowest terms by extracting and canceling out 16.

$$\frac{24562000000}{205379}+\frac{375000000000}{12117361}+\frac{40000}{1.18^{5}}$$

Least common multiple of 205379 and 12117361 is 12117361. Convert \frac{24562000000}{205379} and \frac{375000000000}{12117361} to fractions with denominator 12117361.

$$\frac{1449158000000}{12117361}+\frac{375000000000}{12117361}+\frac{40000}{1.18^{5}}$$

Since \frac{1449158000000}{12117361} and \frac{375000000000}{12117361} have the same denominator, add them by adding their numerators.

$$\frac{1449158000000+375000000000}{12117361}+\frac{40000}{1.18^{5}}$$

Add 1449158000000 and 375000000000 to get 1824158000000.

$$\frac{1824158000000}{12117361}+\frac{40000}{1.18^{5}}$$

Calculate 1.18 to the power of 5 and get 2.2877577568.

$$\frac{1824158000000}{12117361}+\frac{40000}{2.2877577568}$$

Expand \frac{40000}{2.2877577568} by multiplying both numerator and the denominator by 10000000000.

$$\frac{1824158000000}{12117361}+\frac{400000000000000}{22877577568}$$

Reduce the fraction \frac{400000000000000}{22877577568} to lowest terms by extracting and canceling out 32.

$$\frac{1824158000000}{12117361}+\frac{12500000000000}{714924299}$$

Least common multiple of 12117361 and 714924299 is 714924299. Convert \frac{1824158000000}{12117361} and \frac{12500000000000}{714924299} to fractions with denominator 714924299.

$$\frac{107625322000000}{714924299}+\frac{12500000000000}{714924299}$$

Since \frac{107625322000000}{714924299} and \frac{12500000000000}{714924299} have the same denominator, add them by adding their numerators.

$$\frac{107625322000000+12500000000000}{714924299}$$

Add 107625322000000 and 12500000000000 to get 120125322000000.

$$\frac{120125322000000}{714924299}$$

Factor

$$\frac{1453 \cdot 1531 \cdot 2 ^ {7} \cdot 3 ^ {3} \cdot 5 ^ {6}}{59 ^ {5}} = 168025\frac{166660525}{714924299} = 168025.23311632467$$