\(B=\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{192}+\dfrac{2}{384}\)
\(\Leftrightarrow B=\dfrac{2}{3}\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{64}+\dfrac{1}{128}\right)\)
Xét \(A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{64}+\dfrac{1}{128}\)
\(2A=2+1+\dfrac{1}{2}+...+\dfrac{1}{32}+\dfrac{1}{64}\)
\(2A-A=A=2+\dfrac{1}{128}\)
\(\Leftrightarrow B=\dfrac{2}{3}\left(2-\dfrac{1}{128}\right)\)
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