Đáp án:
$\begin{array}{l}
4)\\
a)B = 3 + {3^2} + {3^3} + {3^4} + ... + {3^{60}}\\
= \left( {3 + {3^2}} \right) + \left( {{3^3} + {3^4}} \right) + ... + \left( {{3^{59}} + {3^{60}}} \right)\\
= 3.\left( {1 + 3} \right) + {3^3}.\left( {1 + 3} \right) + ... + {3^{59}}.\left( {1 + 3} \right)\\
= 3.4 + {3^3}.4 + ... + {3^{59}}.4\\
= \left( {3 + {3^3} + ... + {3^{59}}} \right).4 \vdots 4\\
Vay\,B \vdots 4\\
b)B = 3 + {3^2} + {3^3} + {3^4} + ... + {3^{60}}\\
= \left( {3 + {3^2} + {3^3}} \right) + \left( {{3^4} + {3^5} + {3^6}} \right) + ... + \left( {{3^{58}} + {3^{59}} + {3^{60}}} \right)\\
= 3.\left( {1 + 3 + {3^2}} \right) + {3^4}.\left( {1 + 3 + {3^2}} \right) + ... + {3^{58}}.\left( {1 + 3 + {3^2}} \right)\\
= 3.13 + {3^4}.13 + ... + {3^{58}}.13\\
= \left( {3 + {3^4} + ... + {3^{58}}} \right).13 \vdots 13\\
5)a){7^6} + {7^5} - {7^4}\\
= {7^4}.\left( {{7^2} + 7 - 1} \right)\\
= {7^4}.\left( {49 + 7 - 1} \right)\\
= {7^4}.55\\
= {7^4}.5.11 \vdots 11\\
b){8^{10}} - {8^9} - {8^8}\\
= {8^8}.\left( {{8^2} - 8 - 1} \right)\\
= {8^8}.\left( {64 - 9} \right)\\
= {8^8}.55 \vdots 55
\end{array}$
