$\begin{array}{l}
A = 2 + 22 + 222 + 2222 + .... + 222...2(17)\\
A = 2(1 + 11 + 111 + 1111 + ... + 111...1)\\
A = 2\dfrac{{(9 + 99 + 999 + 9999 + ... + 999...9)}}{9}\\
A = 2\dfrac{{(10 - 1 + {{10}^2} - 1 + {{10}^3} - 1 + {{10}^4} - 1 + ... + {{10}^{17}} - 1)}}{9}\\
A = 2\dfrac{{(10 + {{10}^2} + {{10}^3} + {{10}^4} + ... + {{10}^{17}}) - 17}}{9}\\
A = 2\dfrac{{(1 + 10 + {{10}^2} + .... + {{10}^{17}} - 1) - 17}}{9}\\
A = 2\dfrac{{\dfrac{{{{10}^{18}} - 1}}{9} - 18}}{9}\\
A = 2\dfrac{{{\rm{111111111111111111 - 18}}}}{9}\\
A = 2.{\rm{12345679012345677}}\\
{\rm{A = 24691358024691354}}
\end{array}$

               Bài làm

Ta có : A=2+22+222+2222+..+222..22(17 cs 2)

           =2.(1+11+111+...111..111(17 chữ số 1 )

           =2/9.(9+99+999+...+999...99(17 cs 9)

          =2/9.((10-1)+(10^2-1)+(10^3-1)+......+(10^17-1))

         =2/9 .((10+10^2+10^3+...+10^17)-17)

         =2/9.((10^18-10)/9-17)   ≈ 2.469135802x10^16

Vậy .............

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