\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.\dfrac{4}{10}.\dfrac{5}{12}.....\dfrac{30}{62}.\dfrac{31}{64}=2x\)
\(\dfrac{1.2.3.4.5.....30.31}{\left(2.2\right)\left(2.3\right)\left(2.4\right)\left(2.5\right)\left(2.6\right).....\left(2.31\right)\left(2.32\right)}=2x\)
\(\dfrac{1\left(2.3.4.5....30.31\right)}{32\left(2.3.4.5.....31\right).2^{31}}=2x\)
\(\dfrac{1}{2^5.2^{31}}=2x\Rightarrow2x=\dfrac{1}{2^{36}}\Rightarrow x=\dfrac{1}{2^{36}}\div2=\dfrac{1}{2^{37}}\)
Vậy x = \(\dfrac{1}{2^{37}}\)
\(\dfrac{1}{4}\cdot\dfrac{2}{6}\cdot\dfrac{3}{8}\cdot\dfrac{4}{10}\cdot...\cdot\dfrac{30}{62}\cdot\dfrac{31}{64}=2x\\ \dfrac{1}{2\cdot2}\cdot\dfrac{2}{2\cdot3}\cdot\dfrac{3}{2\cdot4}\cdot\dfrac{4}{2\cdot5}\cdot...\cdot\dfrac{30}{2\cdot31}\cdot\dfrac{31}{2\cdot32}=2x\\ \dfrac{1}{2}\cdot\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{30}{31}\cdot\dfrac{31}{32}\right)=2x\\ \dfrac{1}{2}\cdot\left(\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{2\cdot3\cdot4\cdot5\cdot...\cdot31\cdot32}\right)=2x\\ \dfrac{1}{2}\cdot\dfrac{1}{32}=2x\\ 2x=\dfrac{1}{64}\\ x=\dfrac{1}{64}:2\\ x=\dfrac{1}{128}\)
