Solve 2/7(1-2^10)/1-2

$$\frac { \frac { 2 } { 7 } ( 1 - 2 ^ { 10 } ) } { 1 - 2 }$$

Evaluate

$$\frac{2046}{7}\approx 292.285714286$$

Solution Steps

Calculate 2 to the power of 10 and get 1024.

$$\frac{\frac{2}{7}\left(1-1024\right)}{1-2}$$

Subtract 1024 from 1 to get -1023.

$$\frac{\frac{2}{7}\left(-1023\right)}{1-2}$$

Express \frac{2}{7}\left(-1023\right) as a single fraction.

$$\frac{\frac{2\left(-1023\right)}{7}}{1-2}$$

Multiply 2 and -1023 to get -2046.

$$\frac{\frac{-2046}{7}}{1-2}$$

Fraction \frac{-2046}{7} can be rewritten as -\frac{2046}{7} by extracting the negative sign.

$$\frac{-\frac{2046}{7}}{1-2}$$

Subtract 2 from 1 to get -1.

$$\frac{-\frac{2046}{7}}{-1}$$

Express \frac{-\frac{2046}{7}}{-1} as a single fraction.

$$\frac{-2046}{7\left(-1\right)}$$

Multiply 7 and -1 to get -7.

$$\frac{-2046}{-7}$$

Fraction \frac{-2046}{-7} can be simplified to \frac{2046}{7} by removing the negative sign from both the numerator and the denominator.

$$\frac{2046}{7}$$

Factor

$$\frac{2 \cdot 3 \cdot 11 \cdot 31}{7} = 292\frac{2}{7} = 292.2857142857143$$