Question

1/6+1/12+1/20+1/30+.....+1/x.(x+1)=2

Answer 1

Hãy tích cho tui đi

vì câu này dễ mặc dù tui ko biết làm 

Yên tâm khi bạn tích cho tui

Tui sẽ ko tích lại bạn đâu

THANKS

Answer 2

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)

\(\Leftrightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+1}=2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{-3}{2}\)

\(\Leftrightarrow\frac{-3}{-3x-3}=\frac{-3}{2}\)

\(\Leftrightarrow-3x-3=2\)

\(\Leftrightarrow-3x=2+3\)

\(\Leftrightarrow-3x=5\)

\(\Leftrightarrow x=\frac{-5}{3}\)

Vậy \(x=\frac{-5}{3}\)