Solve 50(1-1/102^5)+100/102^5

$$50 ( 1 - \frac { 1 } { 102 ^ { 5 } } ) + \frac { 100 } { 102 ^ { 5 } }$$

Evaluate

$$\frac{276020200825}{5520404016}\approx 50.000000005$$

Solution Steps

Calculate 102 to the power of 5 and get 11040808032.

$$50\left(1-\frac{1}{11040808032}\right)+\frac{100}{102^{5}}$$

Convert 1 to fraction \frac{11040808032}{11040808032}.

$$50\left(\frac{11040808032}{11040808032}-\frac{1}{11040808032}\right)+\frac{100}{102^{5}}$$

Since \frac{11040808032}{11040808032} and \frac{1}{11040808032} have the same denominator, subtract them by subtracting their numerators.

$$50\times \frac{11040808032-1}{11040808032}+\frac{100}{102^{5}}$$

Subtract 1 from 11040808032 to get 11040808031.

$$50\times \frac{11040808031}{11040808032}+\frac{100}{102^{5}}$$

Express 50\times \frac{11040808031}{11040808032} as a single fraction.

$$\frac{50\times 11040808031}{11040808032}+\frac{100}{102^{5}}$$

Multiply 50 and 11040808031 to get 552040401550.

$$\frac{552040401550}{11040808032}+\frac{100}{102^{5}}$$

Reduce the fraction \frac{552040401550}{11040808032} to lowest terms by extracting and canceling out 2.

$$\frac{276020200775}{5520404016}+\frac{100}{102^{5}}$$

Calculate 102 to the power of 5 and get 11040808032.

$$\frac{276020200775}{5520404016}+\frac{100}{11040808032}$$

Reduce the fraction \frac{100}{11040808032} to lowest terms by extracting and canceling out 4.

$$\frac{276020200775}{5520404016}+\frac{25}{2760202008}$$

Least common multiple of 5520404016 and 2760202008 is 5520404016. Convert \frac{276020200775}{5520404016} and \frac{25}{2760202008} to fractions with denominator 5520404016.

$$\frac{276020200775}{5520404016}+\frac{50}{5520404016}$$

Since \frac{276020200775}{5520404016} and \frac{50}{5520404016} have the same denominator, add them by adding their numerators.

$$\frac{276020200775+50}{5520404016}$$

Add 276020200775 and 50 to get 276020200825.

$$\frac{276020200825}{5520404016}$$

Factor

$$\frac{5 ^ {2} \cdot 61 \cdot 103 \cdot 251 \cdot 7001}{2 ^ {4} \cdot 3 ^ {5} \cdot 17 ^ {5}} = 50\frac{25}{5520404016} = 50.00000000452865$$