Solve 100+100999/2+2*1-2^100/1-2

$$100 + \frac { 100999 } { 2 } + 2 \times \frac { 1 - 2 ^ { 100 } } { 1 - 2 }$$

Evaluate

$$\frac{5070602400912917605986812922699}{2}=2.5353012 \cdot 10^{30}$$

Solution Steps

Convert 100 to fraction \frac{200}{2}.

$$\frac{200}{2}+\frac{100999}{2}+2\times \frac{1-2^{100}}{1-2}$$

Since \frac{200}{2} and \frac{100999}{2} have the same denominator, add them by adding their numerators.

$$\frac{200+100999}{2}+2\times \frac{1-2^{100}}{1-2}$$

Add 200 and 100999 to get 101199.

$$\frac{101199}{2}+2\times \frac{1-2^{100}}{1-2}$$

Calculate 2 to the power of 100 and get 1267650600228229401496703205376.

$$\frac{101199}{2}+2\times \frac{1-1267650600228229401496703205376}{1-2}$$

Subtract 1267650600228229401496703205376 from 1 to get -1267650600228229401496703205375.

$$\frac{101199}{2}+2\times \frac{-1267650600228229401496703205375}{1-2}$$

Subtract 2 from 1 to get -1.

$$\frac{101199}{2}+2\times \frac{-1267650600228229401496703205375}{-1}$$

Fraction \frac{-1267650600228229401496703205375}{-1} can be simplified to 1267650600228229401496703205375 by removing the negative sign from both the numerator and the denominator.

$$\frac{101199}{2}+2\times 1267650600228229401496703205375$$

Multiply 2 and 1267650600228229401496703205375 to get 2535301200456458802993406410750.

$$\frac{101199}{2}+2535301200456458802993406410750$$

Convert 2535301200456458802993406410750 to fraction \frac{5070602400912917605986812821500}{2}.

$$\frac{101199}{2}+\frac{5070602400912917605986812821500}{2}$$

Since \frac{101199}{2} and \frac{5070602400912917605986812821500}{2} have the same denominator, add them by adding their numerators.

$$\frac{101199+5070602400912917605986812821500}{2}$$

Add 101199 and 5070602400912917605986812821500 to get 5070602400912917605986812922699.

$$\frac{5070602400912917605986812922699}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 1811 \cdot 45077 \cdot 6901501602235413638813}{2} = 2.5353012004564586 \times 10^{30}$$