$A = 4(1 + 11 + 111 + ... + 11...1)$
$\Rightarrow 9A = 4(9 + 99 + ... + 99...9)$
$= 4\bigg[ 10 - 1 + 10^2 - 1 + ... + 10^9 - 1 \bigg] =4\bigg[ 10 + 10^2 + ... + 10^9 - 9\bigg]$
$= 4\bigg [ 10 + 10^2 + ... + 10^9 \bigg ] - 36$
Ta có $10 + 10^2 + ... + 10^9 $ là 1 CSN với $u_1 = 10,\ q = 10,\ n =9$
Vậy $10 + 10^2 + ... + 10^9 = \dfrac{10(1-10^9)}{1-10} = \dfrac{10^{11} - 10}{9}$
Vậy $9A = 4. \bigg[ \dfrac{10^{11} - 10}{9} -9 \bigg] = 4\dfrac{10^{11} - 91}{9}$
$A = 4\dfrac{10^{11} - 91}{81}$