Question

ai giúp minh giải bài này với ạ:

A=2015/2016+2016/2017+2017/2018+2018/2015

hãy chứng minh rằng A>4

Answer 1

\(A=\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}+\frac{2018}{2015}\)

\(=\frac{2016-1}{2016}+\frac{2017-1}{2017}+\frac{2018-1}{2018}+\frac{2015+3}{2015}\)

\(=1-\frac{1}{2016}+1-\frac{1}{2017}+1-\frac{1}{2018}+1+\frac{3}{2015}\)

\(=4+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2015}-\frac{1}{2017}+\frac{1}{2015}-\frac{1}{2018}\)

mà \(\frac{1}{2015}>\frac{1}{2016};\frac{1}{2017};\frac{1}{2018}\)

\(\Rightarrow A>4\)