Question

1 phần 2 nhân x ,trừ 1 trên 1 phần 2,trừ 1 trên 2 phần 3 -..........trừ1 trên 45.46=-2

Answer 1

\(\frac{1}{2.x}-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{45.46}=-2\)

\(\frac{1}{2.x}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{45.46}\right)=-2\)

\(\frac{1}{2.x}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{45}-\frac{1}{46}\right)=-2\)

\(\frac{1}{2.x}-\left(1-\frac{1}{46}\right)\)

\(\frac{1}{2.x}-\frac{45}{46}=-2\)

\(\frac{1}{2.x}=-2+\frac{45}{46}\)

\(\frac{1}{2.x}=\frac{-47}{46}\)

\(2x=\frac{46}{-47}\)

\(x=\frac{46}{-47}:2=\frac{-23}{47}\)