Đặt \(A=\frac{1}{5}+\left(\frac{1}{5}\right)^2+...+\left(\frac{1}{5}\right)^{50}\)
\(5.A=1+\frac{1}{5}+...+\left(\frac{1}{5}\right)^{49}\)
\(5.A-A=\left(1+\frac{1}{5}+...+\left(\frac{1}{5}\right)^{49}\right)-\left(\frac{1}{5}+\left(\frac{1}{5}\right)^2+...+\left(\frac{1}{5}\right)^{50}\right)\)
\(4.A=1-\frac{1}{5^{50}}< 1\)
\(\Rightarrow A< \frac{1}{4}\)