Đáp án đúng: C
Giải chi tiết:Ta có: \(B = \frac{{2015 + 2016 + 2017}}{{2016 + 2017 + 2018}} = \frac{{2015}}{{2016 + 2017 + 2018}} + \frac{{2016}}{{2016 + 2017 + 2018}} + \frac{{2017}}{{2016 + 2017 + 2018}}\)
Lại có :
\(\begin{array}{l}\frac{{2015}}{{2016}} > \frac{{2015}}{{2016 + 2017 + 2018}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\\frac{{2016}}{{2017}} > \frac{{2016}}{{2016 + 2017 + 2018}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\\frac{{2017}}{{2018}} > \frac{{2017}}{{2016 + 2017 + 2018}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)\end{array}\)
Cộng vế với vế của \((1),\,\,(2),\,\,(3)\) ta suy ra
\(\frac{{2015}}{{2016}} + \frac{{2016}}{{2017}} + \frac{{2017}}{{2018}} > \frac{{2015}}{{2016 + 2017 + 2018}} + \frac{{2016}}{{2016 + 2017 + 2018}} + \frac{{2017}}{{2016 + 2017 + 2018}}\)
Hay \(\frac{{2015}}{{2016}} + \frac{{2016}}{{2017}} + \frac{{2017}}{{2018}} > \frac{{2015 + 2016 + 2017}}{{2016 + 2017 + 2018}}\)
Vậy \(A > B.\)
Chọn C
