$\textit{Đáp án + Giải thích các bước giải:}$
$\text{a) A = 1 + 2 + $2^{2}$ +...+ $2^{4}$}$
$\text{2A = 2(1 + 2 + $2^{2}$ +...+ $2^{4}$)}$
$\text{2A = 2 + $2^{2}$ + $2^{3}$ +...+ $2^{5}$}$
$\text{2A - A = (2 + $2^{2}$ + $2^{3}$ +...+ $2^{5}$) - (1 + 2 + $2^{2}$ +...+ $2^{4}$)}$
$\text{A = $2^{5}$ - 1}$
$\text{Mà B = $2^{5}$ - 1 nên A = B}$
$\text{b) C = 3 + $3^{2}$ + $3^{3}$ +...+ $3^{100}$}$
$\text{3C = 3(3 + $3^{2}$ + $3^{3}$ +...+ $3^{100}$)}$
$\text{3C = $3^{2}$ + $3^{3}$ + $3^{4}$ +...+ $3^{101}$}$
$\text{3C - C = $(3^2 + 3^3 + 3^4 +...+ 3^{101})$ - $(3 + 3^2 + 3^3 +...+ 3^{100})$}$
$\text{2C = $3^{101}$ - 3}$
$\text{C = $\dfrac{3^{101} - 3}{2}$}$
$\text{Mà D = $\dfrac{3^{101} - 3}{2}$ nên C = D}$
