Question

Tìm giá trị của \(x\) biết: \(\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{4}\right)...\left(1+\dfrac{1}{24}\right).\left(1+\dfrac{1}{25}\right).x=26\)

Answer 1

\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)...\left(1+\dfrac{1}{25}\right)\cdot x=26\\ \left(\dfrac{2}{2}+\dfrac{1}{2}\right)\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\left(\dfrac{4}{4}+\dfrac{1}{4}\right)...\left(\dfrac{25}{25}+\dfrac{1}{25}\right)\cdot x=26\\ \dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{26}{25}\cdot x=26\\ \dfrac{\left(3\cdot4\cdot5\cdot...\cdot25\right)\cdot26}{\left(3\cdot4\cdot5\cdot...\cdot25\right)\cdot2}\cdot x=26\\ \dfrac{26}{2}\cdot x=26\\ 13\cdot x=26\\ x=\dfrac{26}{13}\\ x=2\)