Question

[Ngọc Quỳnh]

\(A=\frac{\left(1+17\right)\left(1+\frac{17}{2}\right)\left(1+\frac{17}{3}\right)....\left(1+\frac{17}{19}\right)}{\left(1+19\right)\left(1+\frac{19}{2}\right)\left(1+\frac{19}{3}\right).....\left(1+\frac{19}{17}\right)}\)=?

Answer 1

[Trần Thị Loan]

\(A=\frac{18.\frac{19}{2}.\frac{20}{3}....\frac{36}{19}}{20.\frac{21}{2}.\frac{22}{3}...\frac{36}{17}}=\frac{\frac{18.19.20...36}{1.2.3...17.18.19}}{\frac{20.21.22....36}{1.2.3...17}}=\frac{18.19.\left(20.21...36\right)}{\left(1.2.3...17\right).18.19}.\frac{1.2.3...17}{20.21.22....36}=1\)