Giải thích các bước giải:
a.Ta có:
$A=2+2^2+2^3+...+2^{100}$
$\to 2A=2^2+2^3+2^4+...+2^{101}$
$\to 2 A-A=2^{101}-2$
$\to A=2^{101}-2$
b.Ta có:
$2^2=4$ chia $3$ dư $1$
$\to (2^{2})^{50} $ chia $3$ dư $1$
$\to 2^{2\cdot 50}$ chia $3$ dư $1$
$\to 2^{100}$ chia $3$ dư $1$
$\to 2^{100}\cdot 2$ chia $3$ dư $2$
$\to 2^{101}$ chia $3$ dư $2$
$\to 2^{101}-2\quad\vdots\quad 3$
$\to A\quad\vdots\quad 3$
$\to A∈B(3)$
c.Ta có:
$2^3=8$ chia $7$ dư $1$
$\to (2^3)^{33}$ chia $7$ dư $1$
$\to 2^{3\cdot 33}$ chia $7$ dư $1$
$\to 2^{99}$ chia $7$ dư $1$
$\to 2^{99}\cdot 2^2$ chia $7$ dư $2^2$
$\to 2^{99+2}$ chia $7$ dư $4$
$\to 2^{101}$ chia $7$ dư $4$
$\to 2^{101}-2$ chia $7$ dư $2$
$\to A$ chia $7$ dư $2$
