gọi \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{30}}\)
\(\Leftrightarrow2A=1+\dfrac{1}{2}+...+\dfrac{1}{2^{29}}\)
\(\Leftrightarrow2A-A=(1+\dfrac{1}{2}+...+\dfrac{1}{2^{29}})-\left(\dfrac{1}{2}+...+\dfrac{1}{2^{30}}\right)\)
\(\Leftrightarrow A=1-\dfrac{1}{2^{30}}< 1\)
đpcm