So sánh: a> A= 2015+2016 / 2016+2017 và B= 2015 / 2016 + 2016 / 2017
b> M=2015^35+1 / 2015^34+1 va N= 2015^34+1 / 2015^33+1
c> P= 2015^99+5 / 2015^99-1 va Q= 2015^99 +1 /2015^99
so sánh
a ) A = \(\frac{2015+2016}{2016+2017}\)và B = \(\frac{2015+2016}{2016+2017}\)
b) M = \(\frac{2015^{35}+1}{2015^{34}+1}\)và N = \(\frac{2015^{34}+1}{2015^{33}+1}\)
so sánh:
a) A=\(\frac{2015^{2016}+1}{2015^{2017}+1}\)và B=\(\frac{2015^{2015}+1}{2015^{2016}+1}\)
Vì \(2015^{2016}+1< 2015^{2017}+1\Rightarrow\frac{2015^{2016}+1}{2015^{2017}+1}< 1\)
\(\Rightarrow A=\frac{2015^{2016}+1}{2015^{2017}+1}< \frac{2015^{2016}+1+2014}{2015^{2017}+1+2014}=\frac{2015\left(2015^{2015}+1\right)}{2015\left(2015^{2016}+1\right)}=\frac{2015^{2015}+1}{2015^{2016}+1}=B\)
Vậy \(A< B\)
\(2015A=\frac{2015^{2017}+2015}{2015^{2017}+1}=\frac{2015^{2017}+1+2014}{2015^{2017}+1}=1+\frac{2014}{2015^{2017}+1}\)
\(2015B=\frac{2015^{2016}+2015}{2015^{2016}+1}=\frac{2015^{2016}+1+2014}{2015^{2016}+1}=1+\frac{2014}{2015^{2016}+1}\)
vì \(\frac{2014}{2015^{2017}+1}< \frac{2014}{2015^{2016}+1}\)
nên \(2015A< 2015B\)
=> \(B>A\)
Ta có: 2015^2016+1<2015^2017 +1
=> 2015^2016 +1/ 2015^2017+1 <1
=> A= 2015^2016 +1/ 2015^2017+1 < 2015^2016+1+2014/2015^2017+1+2014=2015^2015+1/2015^2016+1=B
Vậy A<B
---k mk bn nhé--- Lâu rồi mới lên :*
So sanh A=2016^2016+1/2016^2017+1 va B=2016^2015+1/2016^2015+1
so sánh 2 p/s A=2015/2016+2016/2017+2017/2018 va B=2015+2016+2017/2016+2017+2018
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 \(A>B\)
So sánh
\(A=\frac{2015^{2015}+1}{2015^{2016}+1}\)và \(B=\frac{2015^{2016}+1}{2015^{2017}+1}\)
Ta có 20152015 = 20152015
Ta so sánh 20152016+1 và 20152011+1
Vì 20152016 > 20152011
=> 20152016+1 > 20152011 +1
2 phân số có cùng tử số, mẫu của phân số nào nhỏ hơn thì phân số đó lớn hơn
=>\(\frac{2015^{2015}+1}{2015^{2016}+1}
(2015-2014)\(2016\):(2016-2015)\(2020\)
ta thấy \(\frac{2015^{2015}+1}{2015^{2016}+1}\)và \(\frac{2015^{2015}+1}{2015^{2017}+1}\)có cùng từ số là \(2015^{2015}+1\)
do đó ta so sánh \(2015^{2016}+1\)với \(2015^{2017}+1\)
ta thấy 20152016 < 20152017
do đó \(2015^{2016}+1< 2015^{2017}+1\)
\(\frac{2015^{2015}+1}{2015^{2016}+1}>\frac{2015^{2015}+1}{2015^{2017}+1}\)
vì phân số có cùng tử số mẫu số nào lớn hơn thì phân số đó nhỏ hơn
so sánh A=\(\frac{2015^{2016}+1}{2015^{2017}+1}\) và B=\(\frac{2015^{2017}+1}{2015^{2018}+1}\)
Áp dụng tính chất \(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+m}{b+m}\)ta có:
\(B=\frac{2015^{2017}+1}{2015^{2018}+1}< \frac{2015^{2017}+1+2014}{2015^{2018}+1+2014}=\frac{2015^{2017}+2015}{2015^{2018}+2015}\)
\(=\frac{2015\left(2015^{2016}+1\right)}{2015\left(2015^{2017}+1\right)}=\frac{2015^{2016}+1}{2015^{2017}+1}\)
\(\Rightarrow\frac{2015^{2017}+1}{2015^{2018}+1}< \frac{2015^{2016}+1}{2015^{2017}+1}\)
Vậy \(B< A\)
Hay \(A>B\)
So sánh A và B :
A = 2015 . 2016 + 2017 / 2015 . 2016 + 2016
B = 2015 . 2016 + 2018 / 2015 . 2016 + 2017
Đặt 2015.2016+2016=n
suy ra A=(n+1)/n và B=(n+2)/(n+1)
Ta có A - B=(n+1)/n -(n+2)/(n+1)=((n+1)2-n(n+2))/n(n+1)=(n2+2n+1-n2-2n)/n(n+1)=1/n(n+1)
Vì A-B lớn hơn 0 nên A>B
SO SÁNH : A = 2015 mũ 2015 +1 / 2015 mũ 2016 + 1
B = 2015 mũ 2016 + 1 /2015 mũ 2017 + 1
Dễ dàng nhận thấy \(A=\frac{2015^{2015}+1}{2015^{2016}+1}\)cùng tử với \(B=\frac{2015^{2015}+1}{2015^{2017}+1}\)
Ta lại nhận thấy \(2015^{2016}< 2015^{2017}\)
\(\Rightarrow2015^{2016}+1< 2015^{2017}+1\)
Do đó \(\frac{2015^{2015}+1}{2015^{2016}+1}< \frac{2015^{2015}+1}{2015^{2017}+1}\) hay A < B
So sánh a và b biết a=2015^2016-2015^2015 ,b=2015^2017-2015^2016