so sánh 20161/2016 va 20171/2017
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta có \(B=\frac{2015+2016+2017}{2016+2017+2018}\)
\(\Leftrightarrow B=\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\frac{2017}{2016+2017+2018}\)
Vì
\(\frac{2015}{2016}>\frac{2015}{2016+2017+2018};\frac{2016}{2017}>\frac{2016}{2016+2017+2018};\frac{2017}{2018}>\frac{2017}{2016+2017+2018}\) nên \(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}>\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\frac{2017}{2016+2017+2018}\)
Hay \(A>B\)
Ta có : A= ( 26^2017 + 3^2017 )^2016 = 26^2017*2016 + 3^2017*2016 (1) ; B = ( 26^2016+ 3^2016)^2017= 26^2016*2017+ 3^2016*2017 (2) . Từ (1) và (2) suy ra dpcm
A = 2016 x 2016
A = (2015 + 1) x 2016
A = 2015 x 2016 + 2016
B = 2015 x 2017
B = 2015 x (2016 + 1)
B = 2015 x 2016 + 2015
Vì 2016 > 2015
=> A > B
A = \(2016^2\)
B = \(\left(2016-1\right)\left(2016+1\right)=2016\left(2016+1\right)-\left(2016+1\right)\)= \(2016^2+2016-2016-1\)= \(2016^2-1\)
\(\Rightarrow A>B\). Vậy A > B
\(Q=\frac{2015+2016+2017}{2016+2017+2018}=\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\)\(\frac{2017}{2016+2017+2018}\)
ta có :
\(\frac{2015}{2016}>\frac{2015}{2016+2017+2018}\)
\(\frac{2016}{2017}>\frac{2016}{2016+2017+2018}\)
\(\frac{2017}{2018}>\frac{2017}{2016+2017+2018}\)
nên \(P>Q\)
Q=2015+2016+2017/2016+2017+2018=+2018+2016/2016+2017+2018+2017/2016+2017+2018
vì 2015/2016>2015/2016+2017+2018[1]
2016/2017>2016+2017+2018[2]
2017/2018>2016+2017+2018[3]
từ [1] [2] [3] suy ra P>Q
đương nhiên là 2017 lớn hơn rồi