`2x + 1/2 > x - 2/3`

`<=> 2x+ 1/2 - x + 2/3 >0`

`<=> x + 7/6 >0`

`<=> x > -7/6`

Vậy bất phương trình có nghiệm `x> -7/6`

Đặt \(A=\dfrac{5}{2}+\dfrac{5}{4}+\dfrac{5}{8}+...+\dfrac{5}{256}\)

\(\Rightarrow A=5\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\right)\\ \Rightarrow2A=5\left(\dfrac{2}{2}+\dfrac{2}{4}+...+\dfrac{2}{256}\right)\\ \Rightarrow2A=5\left(1+\dfrac{1}{2}+...+\dfrac{1}{128}\right)\\ \Rightarrow2A-A=5\left(1+\dfrac{1}{2}+...+\dfrac{1}{128}\right)-5\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\right)\\ \Rightarrow A=5\left[\left(1+\dfrac{1}{2}+...+\dfrac{1}{128}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\right)\right]\)

\(\Rightarrow A=5\left(1+\dfrac{1}{2}+...+\dfrac{1}{128}-\dfrac{1}{2}-\dfrac{1}{4}-...-\dfrac{1}{256}\right)\\ \Rightarrow A=5\left(1-\dfrac{1}{256}\right)\\ \Rightarrow A=5.\dfrac{255}{256}\\ \Rightarrow A=\dfrac{1275}{256}\)

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