Question

[Hoàng Minh Trí]

Tìm x, biết rằng:

a, \(\dfrac{1}{5\cdot8}\) + \(\dfrac{1}{8\cdot11}\) + \(\dfrac{1}{11\cdot14}\) + ... + \(\dfrac{1}{x\left(x+3\right)}\) = \(\dfrac{101}{1540}\)

b, 1+\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + ... + \(\dfrac{1}{x\left(x+1\right)\div2}\) = \(1\dfrac{1991}{1993}\)

Answer 1

[Hoàng Minh Trí]

Các bạn giúp tớ với, sáng mai mình học rồi.

Answer 2

[Lightning Farron]

a)\(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+\dfrac{1}{11\cdot14}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{101}{1540}\)

\(\Leftrightarrow\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)=\dfrac{101}{1540}\)

\(\Leftrightarrow\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)=\dfrac{101}{1540}\)

\(\Leftrightarrow\dfrac{1}{5}-\dfrac{1}{x+3}=\dfrac{303}{1540}\)\(\Leftrightarrow\dfrac{1}{x+3}=\dfrac{1}{308}\)

\(\Leftrightarrow x+3=308\Leftrightarrow x=305\)