Ta có:
$\text{A = 5 + $5^{2}$ + $5^{3}$ + $5^{4}$ + ... + $5^{9}$ + $5^{10}$}$
$\text{<=> (5 + $5^{2}$) + ($5^{3}$ + $5^{4}$) + ($5^{9}$ + $5^{10}$)}$
$\text{<=> 5(1 + 5) + $5^{3}$(1 + 5) + $5^{9}$(1 + 5)}$
$\text{<=> 6(5 + $5^{3}$ + $5^{9}$) chia hết cho 6 (đpcm)}$