#)Giải :

\(Q=2+\frac{2016}{2017+2018+2019}+\frac{2017}{2017+2018+2019}+\frac{2018}{2017+2018+2019}\)

Ta thấy : \(2>\frac{2016}{2017};2>\frac{2017}{2018};2>\frac{2018}{2019}\left(1\right)\)

\(\frac{2016}{2017+2018+2019}< \frac{2016}{2017}\left(2\right)\)

\(\frac{2017}{2017+2018+2019}< \frac{2017}{2018}\left(3\right)\)

\(\frac{2018}{2017+2018+2019}< \frac{2018}{2019}\left(4\right)\)

Từ (1) (2) (3) (4) \(\Rightarrow P>Q\)

\(\frac{2016}{2017}\)x \(\frac{2017}{2018}\)x \(\frac{2019}{2020}\)=\(\frac{504}{505}\)

đ/s:\(\frac{504}{505}\)

\(\frac{2016}{2017}\cdot\frac{2017}{2018}\cdot\frac{2018}{2019}\cdot\frac{2019}{2020}=\frac{504}{505}\)

\(\frac{2016\cdot2017+2015}{2018\cdot2017-2019}\)

= \(\frac{2016\cdot2017+2015}{\left(2016+2\right)\cdot2017-2019}\)

= \(\frac{2016\cdot2017+2015}{2016\cdot2017+2\cdot2017-2019}\)

= \(\frac{2016\cdot2017+2015}{2016\cdot2017+4034-2019}\)

= \(\frac{2016\cdot2017+2015}{2016\cdot2017-2015}\)

= \(1\)

\(\frac{2016\times2017+2015}{2018\times2017-2019}\)

\(=\frac{2016\times2017+2015}{\left(2016+2\right)\times2017-2019}\)

\(=\frac{2016\times2017+2015}{2016\times2017+2\times2017-2019}\)

\(=\frac{2016\times2017+2015}{2016\times2017+4034-2019}\)

\(=\frac{2016\times2017+2015}{2016\times2017+2015}\)

\(=1\)

Ta có : x = 99

=> 100 = x + 1 

Thay vào A ta có : A = x²⁰¹⁸ - 100x²⁰¹⁷ + 100x²⁰¹⁶ - ...... + 100x² - 100x + 2019

=> A = x²⁰¹⁸ - (x + 1)x²⁰¹⁷ + (x + 1)x²⁰¹⁶ - ...... + (x + 1)x² - (x + 1)x + 2019

=> A = x²⁰¹⁸ - x²⁰¹⁸ - x²⁰¹⁷ + x²⁰¹⁷ + x²⁰¹⁶ -.......+ x³ + x² - x² + x + 2019

=> A = x + 2019

=> A = 99 + 2019

=> A = 2118

P/s : ko cần ! :D 

Theo đề bài ra ta có :

x = 99  

Thay vào A ta có :

A = x²⁰¹⁸ - 100x²⁰¹⁷ + 100x²⁰¹⁶ - ... + 100x² - 100x + 2019

\(\Rightarrow\) A = x²⁰¹⁸ - ( x + 1 ) x²⁰¹⁷ + ( x + 1 ) x²⁰¹⁶ - ... + ( x + 1 ) x² - ( x + 1 ) x + 2019

\(\Rightarrow\) A = x²⁰¹⁸ - x²⁰¹⁸ - x²⁰¹⁷ + x²⁰¹⁷ + x²⁰¹⁶- ... + x³ + x² - x² + x + 2019

\(\Rightarrow\) A = x + 2019

\(\Rightarrow\) A = 99 + 2019

\(\Rightarrow\) A = 2118 

Ta có : 

\(\frac{2016}{2017}>\frac{2016}{2017+2018+2019}\)

\(\frac{2017}{2018}>\frac{2017}{2017+2018+2019}\)

\(\frac{2018}{2019}>\frac{2018}{2017+2018+2019}\)

\(\Rightarrow\frac{2016}{2017}+\frac{2017}{2018}+\frac{2018}{2019}>\) \(\frac{2016}{2017+2018+2019}+\frac{2017}{2017+2018+2019}+\frac{2018}{2017+2018+2019}\)

\(\Rightarrow P>\frac{2016+2017+2018}{2017+2018+2019}\)

\(\Rightarrow P>Q\)

Chúc bạn học tốt !!! 

vì P có các số bé hơn 1 còn Q có các số lớn hơn 1 =>P<Q

Vậy P<Q.

mình làm hơi tắt xin bạn thông cảm bạn tự viết các số có trong P;Q ra nhá