Question

\(\frac{x}{1.3}+\frac{x}{3.5}+\frac{x}{5.7}+...+\frac{x}{39.41}=\frac{1}{41}\)

Answer 1

\(\frac{x}{1\cdot3}+\frac{x}{3\cdot5}+\frac{x}{5\cdot7}+........+\frac{x}{39\cdot41}=\frac{1}{41}\)

\(\Rightarrow x\cdot\left[\frac{1}{2}\cdot\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+.........+\frac{1}{39\cdot41}\right)\right]=\frac{1}{41}\)

\(\Rightarrow x\cdot\left[\frac{1}{2}\cdot\left(1-\frac{1}{41}\right)\right]=\frac{1}{41}\)

\(\Rightarrow x\cdot\left(\frac{1}{2}\cdot\frac{40}{41}\right)=\frac{1}{41}\)

\(\Rightarrow x\cdot\frac{20}{41}=\frac{1}{41}\)

\(\Rightarrow x=\frac{1}{41}:\frac{20}{21}\)

\(\Rightarrow x=\frac{1}{41}\cdot\frac{21}{20}\)

\(\Rightarrow x=\frac{21}{820}\)

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