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

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

Evaluate

$$100$$

Solution Steps

Calculate 101 to the power of 5 and get 10510100501.

$$100\left(1-\frac{1}{10510100501}\right)+\frac{100}{101^{5}}$$

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

$$100\left(\frac{10510100501}{10510100501}-\frac{1}{10510100501}\right)+\frac{100}{101^{5}}$$

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

$$100\times \frac{10510100501-1}{10510100501}+\frac{100}{101^{5}}$$

Subtract 1 from 10510100501 to get 10510100500.

$$100\times \frac{10510100500}{10510100501}+\frac{100}{101^{5}}$$

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

$$\frac{100\times 10510100500}{10510100501}+\frac{100}{101^{5}}$$

Multiply 100 and 10510100500 to get 1051010050000.

$$\frac{1051010050000}{10510100501}+\frac{100}{101^{5}}$$

Calculate 101 to the power of 5 and get 10510100501.

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

Since \frac{1051010050000}{10510100501} and \frac{100}{10510100501} have the same denominator, add them by adding their numerators.

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

Add 1051010050000 and 100 to get 1051010050100.

$$\frac{1051010050100}{10510100501}$$

Divide 1051010050100 by 10510100501 to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$