Question

[Đặng Hoàng Ngọc]

\(\frac{3x}{2.5}+\frac{3x}{5.8}+...+\frac{3x}{14.17}=\frac{1}{21}\)

Answer 1

[caothiquynhmai]

\(\frac{3x}{2\cdot5}+\frac{3x}{5\cdot8}+.........+\frac{3x}{14\cdot17}=\frac{1}{21}\)

\(\Rightarrow3x\cdot\left(\frac{1}{2\cdot5}+\frac{1}{5\cdot7}+........+\frac{1}{14\cdot17}\right)=\frac{1}{21}\)

\(\Rightarrow3x\cdot\left[\frac{1}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot7}+......+\frac{3}{14\cdot17}\right)\right]=\frac{1}{21}\)

\(\Rightarrow3x\cdot\left[\frac{1}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\right]=\frac{1}{21}\)

\(\Rightarrow3x\cdot\left(\frac{1}{3}\cdot\frac{15}{34}\right)=\frac{1}{21}\)

\(\Rightarrow3x\cdot\frac{5}{34}=\frac{1}{21}\)\(\Rightarrow x=\frac{1}{21}:\frac{1}{34}:3\)

\(\Rightarrow x=\frac{34}{315}\)

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