Solve 20000div20.86+20000div20.86^2+20000div20.86^3+20000div20.86^4+20000div20.86^5

$$20000 \div 20.86+20000 \div { 20.86 }^{ 2 } +20000 \div { 20.86 }^{ 3 } +20000 \div { 20.86 }^{ 4 } +20000 \div { 20.86 }^{ 5 }$$

Evaluate

$$\frac{1243003019651000000}{1234302311013443}\approx 1007.049090454$$

Solution Steps

Expand \frac{20000}{20.86} by multiplying both numerator and the denominator by 100.

$$\frac{2000000}{2086}+\frac{20000}{20.86^{2}}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Reduce the fraction \frac{2000000}{2086} to lowest terms by extracting and canceling out 2.

$$\frac{1000000}{1043}+\frac{20000}{20.86^{2}}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Calculate 20.86 to the power of 2 and get 435.1396.

$$\frac{1000000}{1043}+\frac{20000}{435.1396}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Expand \frac{20000}{435.1396} by multiplying both numerator and the denominator by 10000.

$$\frac{1000000}{1043}+\frac{200000000}{4351396}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Reduce the fraction \frac{200000000}{4351396} to lowest terms by extracting and canceling out 4.

$$\frac{1000000}{1043}+\frac{50000000}{1087849}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Least common multiple of 1043 and 1087849 is 1087849. Convert \frac{1000000}{1043} and \frac{50000000}{1087849} to fractions with denominator 1087849.

$$\frac{1043000000}{1087849}+\frac{50000000}{1087849}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Since \frac{1043000000}{1087849} and \frac{50000000}{1087849} have the same denominator, add them by adding their numerators.

$$\frac{1043000000+50000000}{1087849}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Add 1043000000 and 50000000 to get 1093000000.

$$\frac{1093000000}{1087849}+\frac{20000}{20.86^{3}}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Calculate 20.86 to the power of 3 and get 9077.012056.

$$\frac{1093000000}{1087849}+\frac{20000}{9077.012056}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Expand \frac{20000}{9077.012056} by multiplying both numerator and the denominator by 1000000.

$$\frac{1093000000}{1087849}+\frac{20000000000}{9077012056}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Reduce the fraction \frac{20000000000}{9077012056} to lowest terms by extracting and canceling out 8.

$$\frac{1093000000}{1087849}+\frac{2500000000}{1134626507}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Least common multiple of 1087849 and 1134626507 is 1134626507. Convert \frac{1093000000}{1087849} and \frac{2500000000}{1134626507} to fractions with denominator 1134626507.

$$\frac{1139999000000}{1134626507}+\frac{2500000000}{1134626507}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Since \frac{1139999000000}{1134626507} and \frac{2500000000}{1134626507} have the same denominator, add them by adding their numerators.

$$\frac{1139999000000+2500000000}{1134626507}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Add 1139999000000 and 2500000000 to get 1142499000000.

$$\frac{1142499000000}{1134626507}+\frac{20000}{20.86^{4}}+\frac{20000}{20.86^{5}}$$

Calculate 20.86 to the power of 4 and get 189346.47148816.

$$\frac{1142499000000}{1134626507}+\frac{20000}{189346.47148816}+\frac{20000}{20.86^{5}}$$

Expand \frac{20000}{189346.47148816} by multiplying both numerator and the denominator by 100000000.

$$\frac{1142499000000}{1134626507}+\frac{2000000000000}{18934647148816}+\frac{20000}{20.86^{5}}$$

Reduce the fraction \frac{2000000000000}{18934647148816} to lowest terms by extracting and canceling out 16.

$$\frac{1142499000000}{1134626507}+\frac{125000000000}{1183415446801}+\frac{20000}{20.86^{5}}$$

Least common multiple of 1134626507 and 1183415446801 is 1183415446801. Convert \frac{1142499000000}{1134626507} and \frac{125000000000}{1183415446801} to fractions with denominator 1183415446801.

$$\frac{1191626457000000}{1183415446801}+\frac{125000000000}{1183415446801}+\frac{20000}{20.86^{5}}$$

Since \frac{1191626457000000}{1183415446801} and \frac{125000000000}{1183415446801} have the same denominator, add them by adding their numerators.

$$\frac{1191626457000000+125000000000}{1183415446801}+\frac{20000}{20.86^{5}}$$

Add 1191626457000000 and 125000000000 to get 1191751457000000.

$$\frac{1191751457000000}{1183415446801}+\frac{20000}{20.86^{5}}$$

Calculate 20.86 to the power of 5 and get 3949767.3952430176.

$$\frac{1191751457000000}{1183415446801}+\frac{20000}{3949767.3952430176}$$

Expand \frac{20000}{3949767.3952430176} by multiplying both numerator and the denominator by 10000000000.

$$\frac{1191751457000000}{1183415446801}+\frac{200000000000000}{39497673952430176}$$

Reduce the fraction \frac{200000000000000}{39497673952430176} to lowest terms by extracting and canceling out 32.

$$\frac{1191751457000000}{1183415446801}+\frac{6250000000000}{1234302311013443}$$

Least common multiple of 1183415446801 and 1234302311013443 is 1234302311013443. Convert \frac{1191751457000000}{1183415446801} and \frac{6250000000000}{1234302311013443} to fractions with denominator 1234302311013443.

$$\frac{1242996769651000000}{1234302311013443}+\frac{6250000000000}{1234302311013443}$$

Since \frac{1242996769651000000}{1234302311013443} and \frac{6250000000000}{1234302311013443} have the same denominator, add them by adding their numerators.

$$\frac{1242996769651000000+6250000000000}{1234302311013443}$$

Add 1242996769651000000 and 6250000000000 to get 1243003019651000000.

$$\frac{1243003019651000000}{1234302311013443}$$

Factor

$$\frac{604291 \cdot 2056961 \cdot 2 ^ {6} \cdot 5 ^ {6}}{7 ^ {5} \cdot 149 ^ {5}} = 1007\frac{60592460462963}{1234302311013443} = 1007.04909045371$$