\(D=2^{100}-2^{99}-2^{98}-2^{97}-...-2^2-2-1\)

\(D=2^{100}-\left(2^{99}+2^{98}+2^{97}+...+2^2+2+1\right)\)

Đặt \(A=2^{99}+2^{98}+2^{97}+...+2^2+2+1\)

\(2A=2^{100}+2^{99}+2^{98}+...+2^3+2^2+2\)

\(2A-A=\left(2^{100}+2^{99}+2^{98}+...+2^3+2^2+2\right)-\left(2^{99}+2^{98}+2^{97}+...+2^2+2+1\right)\)

\(A=2^{100}-1\)

\(\Rightarrow D=2^{100}-\left(2^{100}-1\right)=2^{100}-2^{100}+1=0+1=1\)

a) A = 1/7.8 + 1/8.9 + 1/9.10 + ... + 1/18.19 + 1/19.20

A = 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + ... + 1/18 - 1/19 + 1/19 - 1/20

A = 1/7 - 1/20

A = 13/140

b) B 2/5.7 + 2/7. 9 + 2/9.11 + .... + 2/17.19 + 2/19.21

B = 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + ... + 1/17 - 1/19 + 1/19 - 1/21

B = 1/5 - 1/21

B = 16/105

a. \(xy+x-y=9\)

\(\Leftrightarrow xy+x-y-1=9-1\)

\(\Leftrightarrow x\left(y+1\right)-\left(y+1\right)=8\)

\(\Leftrightarrow\left(x-1\right)\left(y+1\right)=8\)

Ta có bảng:

Vậy các cặp (x;y) là (2;7) ; (0;-9) ; (3;3) ; (-1;-5) ; (5;1) ; (-3;-3) ; (9;0) ; (-7;-2)

con ba ba