\(A=2^0+2^1+2^2+2^3+.......+2^{100}\)
\(2A=2\left(2^0+2^1+2^2+2^3+..........+2^{100}\right)\)
\(2A=2^1+2^2+2^3+2^4+.......+2^{101}\)
\(2A-A=\left(2^1+2^2+2^3+2^4+........+2^{101}\right)-\left(2^0+2^1+2^2+2^3+..........+2^{100}\right)\)\(2A=2^{101}-2^0=2^{101}-1\)
Ta có : $A=2^0+2^1+2^2+2^3+...+2^{100}$
$=>2A=2^1+2^2+2^3+2^4+...+2^{101}$
$=>2A-A=(2^1+2^2+2^3+...+2^{101})-(2^0+2^1+2^2+...+2^{100})$
$=>A=2^101-2^0=2^101-1$
\(A=2^0+2^1+2^2+.....+2^{100}\)
\(\Rightarrow2A=2^1+2^2+2^3+.......+2^{101}\)
\(\Rightarrow2A-A=\left(2^1+2^2+2^3+.....+2^{101}\right)-\left(2^0+2^1+2^2+.....+2^{100}\right)\)
\(\Rightarrow A=2^{101}-1\)
Chúc bạn học tốt!!!