1+1/3+1/9+1/27+1/81 (ko quy đồng nha)
Không quy đồng
Ta có : \(1+\frac{1}{3}-\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
ta có : \(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(\Rightarrow A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\)
\(\Rightarrow3A=3+1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\)
\(\Rightarrow3A-A=\left(3+1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\right)\)
\(\Rightarrow2A=3-\frac{1}{3^4}\)
\(\Rightarrow A=\left(3-\frac{1}{3^4}\right):2=\frac{121}{81}\)
