So sanh
2015 . 2^3 va 2014 . 3^2^3^2
so sanh a= 2015^2014+1/2015^2014-1 va b= 2015^2014-1/2015^2014-3
\(A=\frac{2015^{2014}+1}{2015^{2014}-1}=\frac{2015^{2014}-1+2}{2015^{2014}-1}=1+\frac{2}{2015^{2014}-1}.\)
\(B=\frac{2015^{2014}-1}{2015^{2014}-3}=\frac{2015^{2014}-3+2}{2015^{2014}-3}=1+\frac{2}{2015^{2014}-3}\)
mà \(\frac{2}{2015^{2014}-1}< \frac{2}{2015^{2014}-3}\)( 20152014 -1 > 20152014 - 3)
\(\Rightarrow A< B\)
so sanh A =(-2)x(-2^2)x(-2^3)x...x(-2^2014) va B=2^2027091
1. So sanh:
2014×2015-2/2013+2013×2014 voi 2014×2015-1/2014×2015
2. Cho a, b, c thuoc N* va a nho hon b.
Hay chung to: a/b nho hon a+c/b+c va 1 nho hon a/a+b +b/b+c+c/a+c
so sanh 2014/2015 va 2015/2016
Bài này ta so sánh theo cách tìm phần bù.
Ta có: 1 - 2014/2015 = 1/2015
1 - 2015/2016 = 1/2016
Vì 1/2015 > 1/2016 nên 2014/2015 < 2015/2016
(phần bù nào có giá trị lớn hơn thì phân số đó bé hơn)
2015/-2014 va -2016/2015 . So sanh]
\(\frac{2015}{-2014}\)>\(\frac{-2016}{2015}\)
So sanh
a) A = 2013. 2015 va B = 20142
b) A = 1030 va B = 2100
c) A = 333444 va B = 444333
d) A = 3450 va B = 5300
So sánh S =2^0+2^2+2^3+...+2^2014 va P = 2^2015
so sanh:
a. 2^70 va 3^51
b. 2015/2017 va 2017/2018
351>350=925>825=275>270
Vì 2017<2018 nên\(\frac{1}{2017}\)>\(\frac{1}{2018}\)
⇒\(\frac{2}{2017}\)>\(\frac{1}{2018}\)
⇒\(\frac{2015}{2017}\)=1-\(\frac{2}{2017}\)<1-\(\frac{1}{2018}\)=\(\frac{2017}{2018}\)
Vậy, \(\frac{2015}{2017}\)< \(\frac{2017}{2018}\)
so sanh \(a=\frac{2013}{2014}+\frac{2014}{2015}\) va \(b=\frac{2013+2014}{2014+2015}\)
\(\frac{3}{x+1}
a = \(\frac{2013}{2014}+\frac{2014}{2015}=\frac{2014-1}{2014}+\frac{2015-1}{2015}\)
\(=1-\frac{1}{2014}+1-\frac{1}{2015}\)
\(=2-\left(\frac{1}{2014}+\frac{1}{2015}\right)>1\) (1)
b = \(\frac{2013+2014}{2014+2015}
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