Question

Cho biểu thức: A= \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2014.2015}\). Tìm giá trị x thỏa mãn: A+\(\frac{1}{2015}=2x\)

Answer 1

\(A=1-\frac{1}{2015}\)

\(A+\frac{1}{2015}=2x\Leftrightarrow1-\frac{1}{2015}+\frac{1}{2015}=2x\Leftrightarrow2x=1\Rightarrow x=\frac{1}{2}\)

Answer 2

A=1\(-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....+\frac{1}{2014}-\frac{1}{2015}\)

=> A= \(1-\frac{1}{2015}\)

A=\(\frac{2014}{2015}\)

A+\(\frac{1}{2015}=2x\)

<=>\(\frac{2014}{2015}+\frac{1}{2015}=2x\)

=>\(2x=1\)

\(=>x=\frac{1}{2}\)