Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
*)\\
B = 5 + {5^2} + {5^3} + {5^4} + ..... + {5^{100}}\\
 = \left( {5 + {5^2}} \right) + \left( {{5^3} + {5^4}} \right) + ..... + \left( {{5^{99}} + {5^{100}}} \right)\\
 = 5.\left( {1 + 5} \right) + {5^3}.\left( {1 + 5} \right) + ..... + {5^{99}}.\left( {1 + 5} \right)\\
 = 5.6 + {5^3}.6 + ..... + {5^{99}}.6\\
 = 6.\left( {5 + {5^3} + .... + {5^{99}}} \right)\,\, \vdots \,\,6\\
*)\\
B = 6.\left( {5 + {5^3} + ..... + {5^{99}}} \right)\\
 = 6.\left[ {\left( {5 + {5^3}} \right) + \left( {{5^5} + {5^7}} \right) + ..... + \left( {{5^{97}} + {5^{99}}} \right)} \right]\\
 = 6.\left[ {5.\left( {1 + {5^2}} \right) + {5^5}.\left( {1 + {5^2}} \right) + ..... + {5^{97}}.\left( {1 + {5^2}} \right)} \right]\\
 = 6.\left[ {5.26 + {5^5}.26 + ..... + {5^{97}}.26} \right]\\
 = 6.26.\left( {5 + {5^5} + ..... + {5^{97}}} \right)\\
 = 156.\left( {5 + {5^5} + ..... + {5^{97}}} \right)\,\, \vdots \,\,156
\end{array}\)

Đáp án:

Giải thích các bước giải:

`+) B(6)`

`B=5+5^2+5^3+5^4+...+5^100`

`=(5+5^2)+(5^3+5^4)+...+(5^99+5^100)`

`= (1+5).5+(1+5).5^3+....+(1+5).5^99`

`=(1+5).(5+5^3+...+5^99)`

`=6.(5+5^3+...+5^99) vdots 6`

`+) B(156)`

`B=6.(5+5^3+...+5^99)`

`=6.[(5+5^3)+(5^5+5^7)+...+(5^97+5^99)]`

`=6.[(1+5^2).5+(1+5^2).5^5+....+(1+5^2).5^97]`

`=6.[26.(5+5^5+...+5^97)]`

`=156.(5+5^5+...+5^97) vdots 156`