Question

[ x - 1/2 ] + [ x - 1/6] + [ x - 1/ 12 ] +...+ [ x - 1/90] = 1

Answer 1

Ta có \(\left(x-\frac{1}{2}\right)+\left(x-\frac{1}{6}\right)+\left(x-\frac{1}{12}\right)+...+\left(x-\frac{1}{90}\right)=1\)

\(\Rightarrow\left(x+x+x+...+x\right)-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)=1\)

\(\Rightarrow9x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{9.10}\right)=1\)

\(\Rightarrow9x-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)=1\)

\(\Rightarrow9x-\left(1-\frac{1}{10}\right)=1\)

\(\Rightarrow9x-\frac{9}{10}=1\)

\(\Rightarrow9x=\frac{19}{10}\)

\(\Rightarrow x=\frac{19}{10}\)