\(A=1+3+3^2+...+3^{100}\)
\(\Rightarrow3A=3+3^2+3^3+...+3^{101}\)
\(\Rightarrow2A=3A-A=3+3^2+...+3^{101}-1-3-...-3^{100}=3^{101}-1\)
\(\Rightarrow2A+1=3^{101}-1+1=3^{101}\)
\(\Rightarrow3^n=3^{101}\Rightarrow n=101\) => Chọn C
\(11,\\ \Rightarrow3A=3+3^2+3^3+...+3^{101}\\ \Rightarrow2A=3^{101}-1\\ \Rightarrow2A+1=3^{101}=3^n\\ \Rightarrow n=101\left(C\right)\\ 41,\)
Diện tích phòng là \(6\cdot6\cdot3=108\left(m^2\right)=1080000\left(cm^2\right)\)
Số gạch cần xài là \(1080000:\left(40\cdot40\right)=675\left(viên\right)\)
Vậy bác cần \(108\cdot30000+675\cdot18000=15390000\left(đồng\right)\left(C\right)\)
