Question

Tính nhanh:

a) (-25) . 68 + (-34) . (-250)

b) B = 2^100 - 2^99 - 2^98 - ... - 2^2 - 2 - 1

Answer 1

a)\(\left(-25\right)\cdot68+\left(-34\right)\cdot\left(-250\right)\)

\(=\left(-25\right)\cdot68+\left(-34\right)\cdot\left(-2\right)\cdot125\)

\(=\left(-25\right)\cdot68+68\cdot125\)

\(=68\left[\left(-25\right)+125\right]\)

\(=68\cdot100=6800\)

b)\(B=2^{100}-2^{99}-...-2^2-2-1\)

\(B=2^{100}-\left(2^{99}+...+2^2+2+1\right)\)

Đặt \(A=2^{99}+...+2^2+2+1\)

\(2A=2\left(2^{99}+...+2^2+2+1\right)\)

\(2A=2^{100}+...+2^3+2^2+2\)

\(2A-A=\left(2^{100}+...+2^3+2^2+2\right)-\left(2^{99}+...+2^2+2+1\right)\)

\(A=2^{100}-1\). Thay A vào B ta có:

\(B=2^{100}-\left(2^{100}-1\right)=2^{100}-2^{100}+1=1\)