Question

Tính:

\(A=\frac{1x2+2x3+3x4+...+2016x2017}{2017x2018}\)

Answer 1

Gọi B = 1x2 + 2 x 3 + 3 x 4 + ... + 2016 x2017

    3B = 3 x ( 1x2 + 2x3 + 3x4 + ... + 2016x2017)

         = 1x2x3 + 2x3x3 + 3x4x3 + ... + 2016x2017x3 )

         = 1x2x3 + 2x3x( 4-1) + 3x4x( 5 -2 ) + ... + 2016x2017x( 2018 - 2015)

         = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 2016x2017x2018 - 2015x2016x2017

         = 2016 x2017 x2018

      B = 672 x2017 x2018

Mà A = \(\frac{672x2017x2018}{2017x2018}\)

         =  672

Vậy A = 672