Bài này nhiều ng` hỏi giờ làm chán lắm rồi, nhưng làm hộ nốt cho bạn.
\(\frac{1}{3}A=\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{11}}\)
\(\Rightarrow\frac{2}{3}A=A-\frac{1}{3}A=\frac{1}{3}-\frac{1}{3^{11}}\)
\(\Rightarrow A=\left(\frac{1}{3}-\frac{1}{3^{11}}\right):\frac{2}{3}=\frac{1}{3}:\frac{2}{3}-\frac{1}{3^{11}}:\frac{2}{3}=\frac{1}{2}-\frac{3}{2.3^{11}}\)
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{10}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^9}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^9}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{10}}\right)\)
\(2A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^9}-\frac{1}{3}-\frac{1}{3^2}-...-\frac{1}{3^{10}}\)
\(2A=1-\frac{1}{3^{10}}\)
\(\Rightarrow A=\frac{1-\frac{1}{3^{10}}}{2}\)
Xin lỗi nha, mk lại chậm hơn Việt mất zùi. Chiều dậy mk mới thấy.