Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
*)\\
A = 7 + {7^2} + {7^3} + ..... + {7^8}\\
= \left( {7 + {7^2}} \right) + \left( {{7^3} + {7^4}} \right) + \left( {{7^5} + {7^6}} \right) + \left( {{7^7} + {7^8}} \right)\\
= 7.\left( {1 + 7} \right) + {7^3}.\left( {1 + 7} \right) + {7^5}.\left( {1 + 7} \right) + {7^7}.\left( {1 + 7} \right)\\
= 7.8 + {7^3}.8 + {7^5}.8 + {7^7}.8\\
= 8.\left( {7 + {7^3} + {7^5} + {7^7}} \right)\\
8\,\, \vdots \,\,2 \Rightarrow 8.\left( {7 + {7^3} + {7^5} + {7^7}} \right)\,\, \vdots \,\,2\\
\Rightarrow A\,\, \vdots \,\,2\\
*)\\
A = 8.\left( {7 + {7^3} + {7^5} + {7^7}} \right)\\
= 8.\left[ {\left( {7 + {7^3}} \right) + \left( {{7^5} + {7^7}} \right)} \right]\\
= 8.\left[ {7.\left( {1 + {7^2}} \right) + {7^5}.\left( {1 + {7^2}} \right)} \right]\\
= 8.\left[ {7.50 + {7^5}.50} \right]\\
= 8.50.\left( {7 + {7^5}} \right)\\
50\,\, \vdots \,\,5 \Rightarrow 8.50.\left( {7 + {7^5}} \right)\,\, \vdots \,\,5\\
\Rightarrow A\,\, \vdots \,\,5
\end{array}\)
