Solve 100(1-1/101^5)+100/101

$$100 ( 1 - \frac { 1 } { 101 ^ { 5 } } ) + \frac { 100 } { 101 }$$

Evaluate

$$\frac{1061416090100}{10510100501}\approx 100.990099$$

Solution Steps

Calculate 101 to the power of 5 and get 10510100501.

$$100\left(1-\frac{1}{10510100501}\right)+\frac{100}{101}$$

Convert 1 to fraction \frac{10510100501}{10510100501}.

$$100\left(\frac{10510100501}{10510100501}-\frac{1}{10510100501}\right)+\frac{100}{101}$$

Since \frac{10510100501}{10510100501} and \frac{1}{10510100501} have the same denominator, subtract them by subtracting their numerators.

$$100\times \frac{10510100501-1}{10510100501}+\frac{100}{101}$$

Subtract 1 from 10510100501 to get 10510100500.

$$100\times \frac{10510100500}{10510100501}+\frac{100}{101}$$

Express 100\times \frac{10510100500}{10510100501} as a single fraction.

$$\frac{100\times 10510100500}{10510100501}+\frac{100}{101}$$

Multiply 100 and 10510100500 to get 1051010050000.

$$\frac{1051010050000}{10510100501}+\frac{100}{101}$$

Least common multiple of 10510100501 and 101 is 10510100501. Convert \frac{1051010050000}{10510100501} and \frac{100}{101} to fractions with denominator 10510100501.

$$\frac{1051010050000}{10510100501}+\frac{10406040100}{10510100501}$$

Since \frac{1051010050000}{10510100501} and \frac{10406040100}{10510100501} have the same denominator, add them by adding their numerators.

$$\frac{1051010050000+10406040100}{10510100501}$$

Add 1051010050000 and 10406040100 to get 1061416090100.

$$\frac{1061416090100}{10510100501}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 2549 \cdot 4164049}{101 ^ {5}} = 100\frac{10406040000}{10510100501} = 100.99009900038634$$