Solve (19/20)^10+1/2(19/20)^9

$$( \frac { 19 } { 20 } ) ^ { 10 } + \frac { 1 } { 2 } ( \frac { 19 } { 20 } ) ^ { 9 }$$

Evaluate

$$\frac{9357943235591}{10240000000000}\approx 0.913861644$$

Solution Steps

Calculate \frac{19}{20} to the power of 10 and get \frac{6131066257801}{10240000000000}.

$$\frac{6131066257801}{10240000000000}+\frac{1}{2}\times \left(\frac{19}{20}\right)^{9}$$

Calculate \frac{19}{20} to the power of 9 and get \frac{322687697779}{512000000000}.

$$\frac{6131066257801}{10240000000000}+\frac{1}{2}\times \frac{322687697779}{512000000000}$$

Multiply \frac{1}{2} times \frac{322687697779}{512000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6131066257801}{10240000000000}+\frac{1\times 322687697779}{2\times 512000000000}$$

Do the multiplications in the fraction \frac{1\times 322687697779}{2\times 512000000000}.

$$\frac{6131066257801}{10240000000000}+\frac{322687697779}{1024000000000}$$

Least common multiple of 10240000000000 and 1024000000000 is 10240000000000. Convert \frac{6131066257801}{10240000000000} and \frac{322687697779}{1024000000000} to fractions with denominator 10240000000000.

$$\frac{6131066257801}{10240000000000}+\frac{3226876977790}{10240000000000}$$

Since \frac{6131066257801}{10240000000000} and \frac{3226876977790}{10240000000000} have the same denominator, add them by adding their numerators.

$$\frac{6131066257801+3226876977790}{10240000000000}$$

Add 6131066257801 and 3226876977790 to get 9357943235591.

$$\frac{9357943235591}{10240000000000}$$

Factor

$$\frac{19 ^ {9} \cdot 29}{2 ^ {20} \cdot 5 ^ {10}} = 0.9138616441006836$$