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