Đáp án:
$\begin{array}{l}
1)a)\\
P = 1 + 6 + {6^2} + {6^3} + ... + {6^{99}}\\
\Rightarrow 6.P = 6 + {6^2} + {6^3} + {6^4} + ... + {6^{100}}\\
\Rightarrow 6P - P = 5P = {6^{100}} - 1\\
\Rightarrow P = \dfrac{{{6^{100}} - 1}}{5}\\
b)Q = 2 + {2^3} + {2^5} + {2^7} + ... + {2^{99}}\\
\Rightarrow {2^2}.Q = 4Q = {2^3} + {2^5} + {2^7} + {2^9} + .. + {2^{101}}\\
\Rightarrow 4Q - Q = {2^{101}} - 2\\
\Rightarrow 3Q = {2^{101}} - 2\\
\Rightarrow Q = \dfrac{{{2^{101}} - 2}}{3}\\
B2)\\
a){x^2} = 4\\
\Rightarrow {x^2} = {2^2} = {\left( { - 2} \right)^2}\\
\Rightarrow \left[ \begin{array}{l}
x = 2\\
x = - 2
\end{array} \right.\\
\text{Vậy}\,x = 2\,\text{hoặc}\,x = - 2\\
b){x^2} = 81\\
\Rightarrow \left[ \begin{array}{l}
x = 9\\
x = - 9
\end{array} \right.\\
\text{Vậy}\,x = 9\,\text{hoặc}\,x = - 9\\
c)6{x^3} - 8 = 40\\
\Rightarrow 6{x^3} = 48\\
\Rightarrow {x^3} = 8\\
\Rightarrow x = 2\\
\text{Vậy}\,x = 2\\
d)\left( {x + 1} \right) = 64\\
\Rightarrow x = 63\\
\text{Vậy}\,x = 63
\end{array}$
