Question

Tìm số tự nhiên x biết:

1/1.2+1/2.3+1/3.4+......+1/x.[x+1]=20/21

Answer 1

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{20}{21}\)

\(1-\dfrac{1}{x+1}\) \(=\dfrac{20}{21}\)

\(\dfrac{1}{x+1}\) \(=\) \(\dfrac{1}{21}\)

\(=>x+1=21\)

\(x=21-1\)

\(x=20\)

Answer 2

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...\dfrac{1}{x.\left(x+1\right)}=\dfrac{20}{21}\)

\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{20}{21}\)

\(1-\dfrac{1}{x+1}=\dfrac{20}{21}\)

\(\Rightarrow\dfrac{1}{x+1}=\dfrac{20}{21}\)

\(\Leftrightarrow x+1=21\)

\(x=21-1\)

\(x=20\)

Vậy \(x=20\)