Question

tìm x

\(\dfrac{x}{1007}-\dfrac{1}{1.2}-\dfrac{1}{2.3}-\dfrac{1}{3.4}-.....-\dfrac{1}{13.14}=\dfrac{15}{14}\)

Answer 1

\(\dfrac{x}{1007}-\dfrac{1}{1.2}-\dfrac{1}{2.3}-\dfrac{1}{3.4}-...-\dfrac{1}{13.14}=\dfrac{15}{14}\)

⇔ \(\dfrac{x}{1007}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{13.14}\right)=\dfrac{15}{14}\)

⇔ \(\dfrac{x}{1007}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{13}-\dfrac{1}{14}\right)=\dfrac{15}{14}\)

⇔ \(\dfrac{x}{1007}-\left(1-\dfrac{1}{14}\right)=\dfrac{15}{14}\)

⇔ \(\dfrac{x}{1007}-\dfrac{13}{14}=\dfrac{15}{14}\)

⇔ \(\dfrac{x}{1007}=\dfrac{15}{14}+\dfrac{13}{14}\)

⇔ \(\dfrac{x}{1007}=\dfrac{28}{14}\)

⇔ \(\dfrac{x}{1007}=2\)

⇔ \(x=2.1007\)

⇔ \(x=2014\)

Vậy \(x=2014\)