Solve 1/1,1+(1-100/(1,1)^10)

$$\frac { 1 } { 1,1 } + ( 1 - \frac { 100 } { ( 1,1 ) ^ { 10 } } )$$

Evaluate

$$-\frac{950483098489}{25937424601}\approx -36,645238034$$

Solution Steps

Expand \frac{1}{1,1} by multiplying both numerator and the denominator by 10.

$$\frac{10}{11}+1-\frac{100}{1,1^{10}}$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{10}{11}+\frac{11}{11}-\frac{100}{1,1^{10}}$$

Since \frac{10}{11} and \frac{11}{11} have the same denominator, add them by adding their numerators.

$$\frac{10+11}{11}-\frac{100}{1,1^{10}}$$

Add 10 and 11 to get 21.

$$\frac{21}{11}-\frac{100}{1,1^{10}}$$

Calculate 1,1 to the power of 10 and get 2,5937424601.

$$\frac{21}{11}-\frac{100}{2,5937424601}$$

Expand \frac{100}{2,5937424601} by multiplying both numerator and the denominator by 10000000000.

$$\frac{21}{11}-\frac{1000000000000}{25937424601}$$

Least common multiple of 11 and 25937424601 is 25937424601. Convert \frac{21}{11} and \frac{1000000000000}{25937424601} to fractions with denominator 25937424601.

$$\frac{49516901511}{25937424601}-\frac{1000000000000}{25937424601}$$

Since \frac{49516901511}{25937424601} and \frac{1000000000000}{25937424601} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49516901511-1000000000000}{25937424601}$$

Subtract 1000000000000 from 49516901511 to get -950483098489.

$$-\frac{950483098489}{25937424601}$$

Factor

$$-\frac{950483098489}{25937424601} = -36\frac{16735812853}{25937424601} = -36.64523803386226$$