Đáp án:

$\begin{array}{l}
b)\\
B = 4 + {4^2} + {4^3} + ... + {4^{2016}}\\
 = \left( {4 + {4^2}} \right) + \left( {{4^3} + {4^4}} \right) + ... + \left( {{4^{2015}} + {4^{2016}}} \right)\\
 = 4.\left( {1 + 4} \right) + {4^3}.\left( {1 + 4} \right) + ... + {4^{2015}}\left( {1 + 4} \right)\\
 = 5.\left( {4 + {4^3} + .. + {4^{2015}}} \right) \vdots 5\\
B = 4 + {4^2} + {4^3} + ... + {4^{2016}}\\
 = \left( {4 + {4^2} + {4^3}} \right) + ... + \left( {{4^{2014}} + {4^{2015}} + {4^{2016}}} \right)\\
 = 4.\left( {1 + 4 + {4^2}} \right) + ... + {4^{2014}}.\left( {1 + 4 + {4^2}} \right)\\
 = 4.21 + {4^4}.21 + ... + {4^{2014}}.21\\
 = \left( {4 + {4^4} + ... + {4^{2014}}} \right).21 \vdots 21\\
B = 4 + {4^2} + {4^3} + ... + {4^{2016}}\\
 = \left( {4 + {4^2} + {4^3} + {4^4}} \right) + ... + \\
\left( {{4^{2013}} + {4^{2014}} + {4^{2015}} + {4^{2016}}} \right)\\
 = 4.\left( {1 + 4 + {4^2} + {4^3}} \right) + ... + {4^{2013}}.\left( {1 + 4 + {4^2} + {4^3}} \right)\\
 = 4.85 + {4^5}.85 + ... + {4^{2013}}.85\\
 = \left( {4 + {4^5} + ... + {4^{2013}}} \right).85 \vdots 85
\end{array}$

Đáp án:  `B` $\vdots$ `5 ; 21 ; 85`

Giải thích các bước giải:

`+) B = 4 + 4^2 + 4^3 + 4^4 + ... + 4^2016`

`= (4 + 4^2) + (4^3 + 4^4) + ... + (4^2015 + 4^2016)`

`= 4(1 + 4) + 4^3(1 + 4) + ... + 4^2015(1 + 4)`

`= 4 . 5 + 4^3 . 5 + ... + 4^2015 . 5`

`= (4 + 4^3 + ... + 4^2015) . 5` $\vdots$ `5`   `(đpcm)`

`+) B = 4 + 4^2 + 4^3 + 4^4 + ... + 4^2016`

`= (4 + 4^2 + 4^3) + (4^4 + 4^5 + 4^6) + ... + (4^2014 + 4^2015 + 4^2016)`

`= 4(1 + 4 + 4^2) + 4^4(1 + 4 + 4^2) + ... + 4^2014(1 + 4 + 4^2)`

`= 4 . 21 + 4^4 . 21 + ... + 4^2014 . 21`

`= (4 + 4^4 + ... + 4^2014) . 21` $\vdots$ `21`   `(đpcm)`

`+) B = 4 + 4^2 + 4^3 + 4^4 + ... + 4^2016`

`= (4 + 4^2 + 4^3 + 4^4) + ... + (4^2013 + 4^2014 + 4^2015 + 4^2016)`

`= 4(1 + 4 + 4^2 + 4^3) + ... + 4^2013(1 + 4 + 4^2 + 4^3)`

`= 4 . 85 + ... + 4^2013 . 85`

`= (4 + ... + 4^2013) . 85` $\vdots$ `85`   `(đpcm)`