Question

Tìm x, biết:

\(\)|x+\(\dfrac{1}{2}\)|+|x+\(\dfrac{1}{6}\)|+\(\left|x+\dfrac{1}{12}\right|\)+\(\left|x+\dfrac{1}{20}\right|\)+...+\(\left|x+\dfrac{1}{110}\right|\)=11x

Answer 1

\(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{6}\right|+...+\left|x+\dfrac{1}{110}\right|=11x\left(đk:x\ge0\right)\)

\(\Leftrightarrow x+\dfrac{1}{2}+x+\dfrac{1}{6}+x+\dfrac{1}{12}+...+x+\dfrac{1}{110}=11x\)

\(\Leftrightarrow10x+\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{10.11}\right)=11x\)

\(\Leftrightarrow x=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)

\(\Leftrightarrow x=1-\dfrac{1}{11}=\dfrac{10}{11}\left(tm\right)\)