Solve 32500/113+32500/113^2+32500/113^3+32500/113^4+frac{32500}{113^5}-110000

$$\frac{ 32500 }{ 113 } + \frac{ 32500 }{ { 113 }^{ 2 } } + \frac{ 32500 }{ { 113 }^{ 3 } } + \frac{ 32500 }{ { 113 }^{ 4 } } + \frac{ 32500 }{ { 113 }^{ 5 } } -110000$$

Evaluate

$$-\frac{2021332345147500}{18424351793}\approx -109709.821428587$$

Solution Steps

Calculate 113 to the power of 2 and get 12769.

$$\frac{32500}{113}+\frac{32500}{12769}+\frac{32500}{113^{3}}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Least common multiple of 113 and 12769 is 12769. Convert \frac{32500}{113} and \frac{32500}{12769} to fractions with denominator 12769.

$$\frac{3672500}{12769}+\frac{32500}{12769}+\frac{32500}{113^{3}}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Since \frac{3672500}{12769} and \frac{32500}{12769} have the same denominator, add them by adding their numerators.

$$\frac{3672500+32500}{12769}+\frac{32500}{113^{3}}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Add 3672500 and 32500 to get 3705000.

$$\frac{3705000}{12769}+\frac{32500}{113^{3}}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Calculate 113 to the power of 3 and get 1442897.

$$\frac{3705000}{12769}+\frac{32500}{1442897}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Least common multiple of 12769 and 1442897 is 1442897. Convert \frac{3705000}{12769} and \frac{32500}{1442897} to fractions with denominator 1442897.

$$\frac{418665000}{1442897}+\frac{32500}{1442897}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Since \frac{418665000}{1442897} and \frac{32500}{1442897} have the same denominator, add them by adding their numerators.

$$\frac{418665000+32500}{1442897}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Add 418665000 and 32500 to get 418697500.

$$\frac{418697500}{1442897}+\frac{32500}{113^{4}}+\frac{32500}{113^{5}}-110000$$

Calculate 113 to the power of 4 and get 163047361.

$$\frac{418697500}{1442897}+\frac{32500}{163047361}+\frac{32500}{113^{5}}-110000$$

Least common multiple of 1442897 and 163047361 is 163047361. Convert \frac{418697500}{1442897} and \frac{32500}{163047361} to fractions with denominator 163047361.

$$\frac{47312817500}{163047361}+\frac{32500}{163047361}+\frac{32500}{113^{5}}-110000$$

Since \frac{47312817500}{163047361} and \frac{32500}{163047361} have the same denominator, add them by adding their numerators.

$$\frac{47312817500+32500}{163047361}+\frac{32500}{113^{5}}-110000$$

Add 47312817500 and 32500 to get 47312850000.

$$\frac{47312850000}{163047361}+\frac{32500}{113^{5}}-110000$$

Calculate 113 to the power of 5 and get 18424351793.

$$\frac{47312850000}{163047361}+\frac{32500}{18424351793}-110000$$

Least common multiple of 163047361 and 18424351793 is 18424351793. Convert \frac{47312850000}{163047361} and \frac{32500}{18424351793} to fractions with denominator 18424351793.

$$\frac{5346352050000}{18424351793}+\frac{32500}{18424351793}-110000$$

Since \frac{5346352050000}{18424351793} and \frac{32500}{18424351793} have the same denominator, add them by adding their numerators.

$$\frac{5346352050000+32500}{18424351793}-110000$$

Add 5346352050000 and 32500 to get 5346352082500.

$$\frac{5346352082500}{18424351793}-110000$$

Convert 110000 to fraction \frac{2026678697230000}{18424351793}.

$$\frac{5346352082500}{18424351793}-\frac{2026678697230000}{18424351793}$$

Since \frac{5346352082500}{18424351793} and \frac{2026678697230000}{18424351793} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5346352082500-2026678697230000}{18424351793}$$

Subtract 2026678697230000 from 5346352082500 to get -2021332345147500.

$$-\frac{2021332345147500}{18424351793}$$

Factor

$$-\frac{2021332345147500}{18424351793} = -109709\frac{15134289263}{18424351793} = -109709.82142858718$$