Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a, Ta có: \(\dfrac{2016}{2017+2018}< \dfrac{2016}{2017}\)
\(\dfrac{2017}{2017+2018}< \dfrac{2017}{2018}\)
\(\Rightarrow A=\dfrac{2016+2017}{2017+2018}< B=\dfrac{2016}{2017}+\dfrac{2017}{2018}\)
Vậy A < B
b, Ta có: \(\dfrac{2017}{2016+2017}< \dfrac{2017}{2016}\)
\(\dfrac{2018}{2016+2017}< \dfrac{2018}{2017}\)
\(\Rightarrow M=\dfrac{2017+2018}{2016+2017}< N=\dfrac{2017}{2016}+\dfrac{2018}{2017}\)
Vậy M < N
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
\(A=\dfrac{\dfrac{1}{2017}+\dfrac{2}{2016}+\dfrac{3}{2015}+...+\dfrac{2016}{2}+\dfrac{2017}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{1}{2018}}\)
\(A=\dfrac{\left(\dfrac{1}{2017}+1\right)+\left(\dfrac{2}{2016}+1\right)+\left(\dfrac{3}{2015}+1\right)+...+\left(\dfrac{2016}{2}+1\right)+1}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{1}{2018}}\)
\(A=\dfrac{\dfrac{2018}{2017}+\dfrac{2018}{2016}+\dfrac{2018}{2015}+...+\dfrac{2018}{2}+\dfrac{2018}{2018}}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{1}{2018}}\)
\(A=\dfrac{2018\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{1}{2018}\right)}{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{1}{2018}}=2018\)
Giải:
Ta có:
\(P=\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}\)
và \(Q=\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}\)
Vì \(\left\{{}\begin{matrix}\dfrac{2016}{2017}=\dfrac{2016}{2017}\\\dfrac{2017}{2018}=\dfrac{2017}{2018}\\\dfrac{2018}{2019}=\dfrac{2018}{2019}\end{matrix}\right.\)
\(\Leftrightarrow\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}=\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}\)
Hay \(P=Q\)
Vậy ...
\(A=\frac{10^{2016}+2018}{10^{2017}+2018}\)
\(\Rightarrow10A=\frac{10^{2017}+20180}{10^{2017}+2018}\)
\(=\frac{10^{2017}+2018+18162}{10^{2017}+2018}\)
\(=\frac{10^{2017}+2018}{10^{2017}+2018}+\frac{18162}{10^{2017}+2018}\)
\(=1+\frac{18162}{10^{2017}+2018}\)
\(B=\frac{10^{2017}+2018}{10^{2018}+2018}\)
\(\Rightarrow10B=\frac{10^{2018}+20180}{10^{2018}+2018}\)
\(=\frac{10^{2018}+2018+18162}{10^{2018}+2018}\)
\(=\frac{10^{2018}+2018}{10^{2018}+2018}+\frac{18162}{10^{2018}+2018}\)
\(=1+\frac{18162}{10^{2018}+2018}\)
Ta thấy: \(1+\frac{18162}{10^{2017}+2018}>1+\frac{18162}{10^{2018}+2018}\)
=> 10A > 10B
=> A > B
Ta có:2015/2016>2015/2016+2017+2018
2016/2017>2016/2016+2017+2018
2017/2018>2017/2016+2017+2018-Mình áp dụng so sánh phân số cùng tử đấy.
Suy ra2015/2016+2016/2017+2017/2018>(2015+2016+2017)/(2016+2017+2018)=B
\(A=\frac{2017^{2018+1}}{2017^{2018-3}}\)và \(B=\frac{2017^{2018-1}}{2017^{2018-5}}\)
Có \(A=\frac{2017^{2019}}{2017^{2015}}\)và \(B=\frac{2017^{2017}}{2017^{2013}}\)
Mà\(\frac{2017^{2019}}{2017^{2015}}>\frac{2017^{2018}}{2017^{2015}}\)và\(\frac{2017^{2017}}{2017^{2013}}>\frac{2017^{2017}}{2017^{2015}}\)
Vì \(\frac{2017^{2018}}{2017^{2015}}>\frac{2017^{2017}}{2017^{2015}}\)
Vậy A>B
B = \(\frac{2015+2016+2017}{2016+2017+2018}=\frac{2016.3}{2017.3}=\frac{2016}{2017}\left(1\right)\)
Mà A = \(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}.\left(2\right)\)
Từ \(\left(1\right)\)và \(\left(2\right)\)=> A > B.
Vậy A > B .
Bạn Dont look at me
Bạn nên làm theo bạn ấy
Bạn k đúng cho bạn ấy. Bởi vì bạn ấy làm đúng
Theo mk là vậy
Ta có :
\(M=\dfrac{2018^{2017}+1}{2018^{2018}+1}< 1\)
\(\Rightarrow M< \dfrac{2018^{2017}+1+2017}{2017^{2018}+1+2017}=\dfrac{2018^{2017}+2018}{2017^{2018}+2018}=\dfrac{2018\left(2018^{2016}+1\right)}{2018\left(2018^{2017}+1\right)}=\dfrac{2018^{2016}+1}{2018^{2017}+1}=N\)
\(\Rightarrow M< N\)
Giải:
Ta có:
\(2018M=\dfrac{\left(2018^{2017}+1\right)2018}{2018^{2018}+1}.\)
\(2018M=\dfrac{2018^{2018}+2018}{2018^{2018}+1}.\)
\(2018M=\dfrac{\left(2018^{2018}+1\right)+2017}{2018^{2018}+1}.\)
\(2018M=\dfrac{2018^{2018}+1}{2018^{2018}+1}+\dfrac{2017}{2018^{2018}+1}.\)
\(2018M=1+\dfrac{2017}{2018^{2018}+1}._{\left(1\right)}\)
Ta lại có:
\(2018N=\dfrac{\left(2018^{2016}+1\right)2018}{2018^{2017}+1}.\)
\(2018N=\dfrac{2018^{2017}+2018}{2018^{2017}+1}.\)
\(2018N=\dfrac{\left(2018^{2017}+1\right)+2017}{2018^{2017}+1}.\)
\(2018N=\dfrac{2018^{2017}+1}{2018^{2017}+1}+\dfrac{2017}{2018^{2017}+1}.\)
\(2018N=1+\dfrac{2017}{2018^{2017}+1}._{\left(2\right)}\)
Và \(\dfrac{2017}{2018^{2018}+1}< \dfrac{2017}{2018^{2017}+1}._{\left(3\right)}\)
Từ \(_{\left(1\right);\left(2\right)}\) và \(_{\left(3\right)}\Rightarrow2018M< 2018N\Rightarrow M< N.\)
Vậy......
~ Học tốt!!! ~