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

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

\(\left(1-\dfrac{1}{50}\right).x=1\)

\(\dfrac{49}{50}\cdot x=1\)

\(x=1\div\dfrac{49}{50}\)

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

So x = \(\dfrac{50}{49}\)

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

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

\(\Leftrightarrow\left(1-\dfrac{1}{50}\right).x=1\Leftrightarrow\dfrac{49}{50}x=1\Leftrightarrow x=\dfrac{50}{49}\)