Question

(1/1.2+1/2.3+1/3.4+…+1/49.50)x=49/50

Answer 1

Đug r pn

có cần chi tiết hơn k

Answer 2

\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..+\frac{1}{49.50}\right)x=\frac{49}{50}\)

\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\right)x=\frac{49}{50}\)

\(\left(1-\frac{1}{50}\right)x=\frac{49}{50}\)

\(\frac{49}{50}x=\frac{49}{50}\)

\(x=\frac{\frac{49}{50}}{\frac{49}{50}}\)

\(x=1\)

Vậy \(x=1\)

Answer 3

Gọi A=1/1.2+1/2.3+1/3.4+...+1/49.50

A=1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50

A=1-1/50

A=49/50

Viết lại ta có: (1/1.2+1/2.3+1/3.4+...+1/49.50)x=49/50

                 49/50x=49/50

               => x=1

Answer 4

\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\cdot x=\frac{49}{50}\)

\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\cdot x=\frac{49}{50}\)

\(\left(1-\frac{1}{50}\right)\cdot x=\frac{49}{50}\)

\(\frac{49}{50}\cdot x=\frac{49}{50}\)

\(\Rightarrow x=1\)