Question

A.1=(1+1/2) . (1+1/3) . (1+1/4). ...... . (1+1/2017)

Giups mik đi nha. Mai mik cần rùi

Answer 1

Ta có: 

\(A=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).....\left(1+\frac{1}{2017}\right)\)

    \(=\left(\frac{2}{2}+\frac{1}{2}\right).\left(\frac{3}{3}+\frac{1}{3}\right).\left(\frac{4}{4}+\frac{1}{4}\right).....\left(\frac{2027}{2017}+\frac{1}{2017}\right)\)

     \(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{2018}{2017}\)

      \(=\frac{2.4.5.....2018}{2.3.4.....2017}\)

       \(=\frac{2018}{2}=1009\)