Solve 40000div1.1+50000div1.1^2+30000div1.1^3+50000div1.1^4-100000

$$40000 \div 1.1+50000 \div { 1.1 }^{ 2 } +30000 \div { 1.1 }^{ 3 } +50000 \div { 1.1 }^{ 4 } -100000$$

Evaluate

$$\frac{503300000}{14641}\approx 34376.067208524$$

Solution Steps

Expand \frac{40000}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{400000}{11}+\frac{50000}{1.1^{2}}+\frac{30000}{1.1^{3}}+\frac{50000}{1.1^{4}}-100000$$

Calculate 1.1 to the power of 2 and get 1.21.

$$\frac{400000}{11}+\frac{50000}{1.21}+\frac{30000}{1.1^{3}}+\frac{50000}{1.1^{4}}-100000$$

Expand \frac{50000}{1.21} by multiplying both numerator and the denominator by 100.

$$\frac{400000}{11}+\frac{5000000}{121}+\frac{30000}{1.1^{3}}+\frac{50000}{1.1^{4}}-100000$$

Least common multiple of 11 and 121 is 121. Convert \frac{400000}{11} and \frac{5000000}{121} to fractions with denominator 121.

$$\frac{4400000}{121}+\frac{5000000}{121}+\frac{30000}{1.1^{3}}+\frac{50000}{1.1^{4}}-100000$$

Since \frac{4400000}{121} and \frac{5000000}{121} have the same denominator, add them by adding their numerators.

$$\frac{4400000+5000000}{121}+\frac{30000}{1.1^{3}}+\frac{50000}{1.1^{4}}-100000$$

Add 4400000 and 5000000 to get 9400000.

$$\frac{9400000}{121}+\frac{30000}{1.1^{3}}+\frac{50000}{1.1^{4}}-100000$$

Calculate 1.1 to the power of 3 and get 1.331.

$$\frac{9400000}{121}+\frac{30000}{1.331}+\frac{50000}{1.1^{4}}-100000$$

Expand \frac{30000}{1.331} by multiplying both numerator and the denominator by 1000.

$$\frac{9400000}{121}+\frac{30000000}{1331}+\frac{50000}{1.1^{4}}-100000$$

Least common multiple of 121 and 1331 is 1331. Convert \frac{9400000}{121} and \frac{30000000}{1331} to fractions with denominator 1331.

$$\frac{103400000}{1331}+\frac{30000000}{1331}+\frac{50000}{1.1^{4}}-100000$$

Since \frac{103400000}{1331} and \frac{30000000}{1331} have the same denominator, add them by adding their numerators.

$$\frac{103400000+30000000}{1331}+\frac{50000}{1.1^{4}}-100000$$

Add 103400000 and 30000000 to get 133400000.

$$\frac{133400000}{1331}+\frac{50000}{1.1^{4}}-100000$$

Calculate 1.1 to the power of 4 and get 1.4641.

$$\frac{133400000}{1331}+\frac{50000}{1.4641}-100000$$

Expand \frac{50000}{1.4641} by multiplying both numerator and the denominator by 10000.

$$\frac{133400000}{1331}+\frac{500000000}{14641}-100000$$

Least common multiple of 1331 and 14641 is 14641. Convert \frac{133400000}{1331} and \frac{500000000}{14641} to fractions with denominator 14641.

$$\frac{1467400000}{14641}+\frac{500000000}{14641}-100000$$

Since \frac{1467400000}{14641} and \frac{500000000}{14641} have the same denominator, add them by adding their numerators.

$$\frac{1467400000+500000000}{14641}-100000$$

Add 1467400000 and 500000000 to get 1967400000.

$$\frac{1967400000}{14641}-100000$$

Convert 100000 to fraction \frac{1464100000}{14641}.

$$\frac{1967400000}{14641}-\frac{1464100000}{14641}$$

Since \frac{1967400000}{14641} and \frac{1464100000}{14641} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1967400000-1464100000}{14641}$$

Subtract 1464100000 from 1967400000 to get 503300000.

$$\frac{503300000}{14641}$$

Factor

$$\frac{7 \cdot 719 \cdot 2 ^ {5} \cdot 5 ^ {5}}{11 ^ {4}} = 34376\frac{984}{14641} = 34376.06720852401$$