## A=2015/2016+2016/2017+2017/2018+2018/2015 chứng minh A lớn hơn 4

Question

A=2015/2016+2016/2017+2017/2018+2018/2015 chứng minh A lớn hơn 4

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3 tháng 2021-09-08T07:32:21+00:00 2 Answers 6 views 0

1. Đáp án:

Giải thích các bước giải:

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})

=4+\frac{2016-2015}{2015.2016}+\frac{2017-2015}{2015.2017}+\frac{2018-2015}{2015.2018}

=4+\frac{1}{2015.2016}+\frac{2}{2015.2017}+\frac{3}{2015.2018}

>4+0+0+0=4(đpcm)

2. Đáp án:

A>4

Giải thích các bước giải:

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

A=2016-12016+2017-12017+2018-12018+2015+32015

A=1-1/2016+1-1/2017+1-1/2018+1+3/2015

A=4+(1/2015-1/2016)+(1/2015-1/2017)+(1/2015-1/2018)

A=4+2016-20152015.2016+2017-20152015.2017+2018-20152015.2018

A=4+1/2015.2016+2/2015.2017+3/2015.2018