Question

So Sánh: A= 1/3  + 1/(3^2) + ... +1/(3^50) với 1/2

Answer 1

\(3A=1+\frac{1}{3}+...+\frac{1}{3^{49}}\)

\(3A-A=\left(1+\frac{1}{3}+...+\frac{1}{3^{49}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{50}}\right)\)

\(2A=1-\frac{1}{3^{50}}< 1\)

\(A< \frac{1}{2}\)