So sanh 2016 /2017+2017/2018 voi 1
Những câu hỏi liên quan
Cho A= \(\frac{2016}{2017}+\frac{2017}{2018}+\frac{2018}{2016}\)
So sanh A voi 3
a. So sanh 2 phan so:A= 2015/2016+2016/2017+2017/2018 va B = 2015+2016+2017/2016+2017+2018
b.1/2.4+1/4.6+........+1/(2x-2).2x = 1/8
c.Cho A = 1/4+1/9+1/16+...+1/81+1/100 . Chung minh rang : A > 65/132
d.Cho B = 12/(2 . 4 ) ^ 2 + 20/ (4 . 6) ^2 + ...........+ 388/ ( 96 . 98 ) ^ 2 + 396/ ( 98 . 100 ) ^2 .Hay so sanh B voi 1 /4
so sanh
A=2016/2017+2017/2018 va B=2016+2017/2017+2018
So sánh \(A=\dfrac{2016}{2017}+\dfrac{2017}{2018}\) và \(B=\dfrac{2016+2017}{2017+2018}\)
Có 2 cách:
C1 :Rảnh thì bấm máy tính luôn rồi so sánh (nhưng cách này tỉ lệ sai khá cao nếu bất cẩn ghi nhầm số):
\(A=\dfrac{2016}{2017}+\dfrac{2017}{2018}\) \(=1,999008674\approx2\)
\(B=\dfrac{2016+2017}{2017+2018}\) \(=0,9995043371\approx1\)
Do 2 > 1 nên :
\(\Rightarrow A>B\).
C2:
Ta có:
\(\dfrac{2016}{2017}>\dfrac{2016}{2018}\Rightarrow A>\dfrac{2016}{2018}+\dfrac{2017}{2018}\Rightarrow A>\dfrac{2016+2017}{2017}\)
\(B=\dfrac{2016+2017}{2017+2018}=\dfrac{2016+2017}{4035}\)
Vì \(\dfrac{2016+2017}{2018}>\dfrac{2016+2017}{4035}\)
\(\Rightarrow A>B\).
_ Học tốt :))_
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So sanh :\(\frac{2017}{2018}+\frac{2018}{2019}va\frac{2015}{2016}+\frac{2016}{2017}\)
so sanh 2016^2017 va 2017^2016
giup to voi!!!
so sanh
\(\frac{2016+2017}{2017+2018}\) va \(\frac{2016}{2017}\)+ \(\frac{2017}{2018}\)
ta xét \(\frac{2016}{2017}+\frac{2017}{2018}=\frac{2016.2018}{2017.2018}+\frac{2017.2017}{2017.2018}\)
\(=\frac{2016.2018+2017.2017}{2017.2018}\)
Ta thấy \(2016+2017< 2016.2018+2017.2017\)
và \(2017+2018< 2017.2018\)
\(\Rightarrow\frac{2016+2017}{2017+2017}< \frac{2016}{2017}+\frac{2017}{2018}\)
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lấy 2016+2017/2017+2018-2016/2017+2017/2018=0.(9)==>2016+2017/2017+2018>2016/2017+2017/2018
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so sanh
A=\(\frac{2016^{2016}+1}{2016^{2017}+1}\)
B=\(\frac{2016^{2017}-3}{2016^{2018}-3}\)
\(A=\frac{2016^{2016}+1}{2016^{2017}+1}\Rightarrow2016A=\frac{2016^{2017}+2016}{2016^{2017}+1}=1+\frac{2015}{2016^{2017}+1}\)
\(B=\frac{2016^{2017}-3}{2016^{2018}-3}\Rightarrow2016B=\frac{2016^{2018}-6048}{2016^{2018}-3}=1+\frac{-6045}{2016^{2018}-3}\)
Vì \(\frac{2015}{2016^{2017}+1}>0;\frac{-6045}{2016^{2018}-3}< 0\)
Nên: A>B
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cho mk hoi con cach giai nao khac ko z??
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2016A=\(\frac{2016^{2017}+2016}{2016^{2017}+1}\Rightarrow1+\frac{2016}{2016^{2017}+1}\)
2016B=\(\frac{2016^{2018}-2016}{2016^{2018}-3}\Rightarrow1-\frac{2016}{2016^{2018}-3}\)
\(\Rightarrow\)2016A>2016B\(\Rightarrow\)A>B
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Tinh A= 2014/2015+2015/2016+2016/2017+2017/2014 hay so sanh A voi 4
=(2014/2014)+(2015+2015)+(2016/2016)+(2017+2017)
=1+1+1+1
=4
vậy A=4 (4=4)
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so sanh
A=\(\frac{2016^{2016}+1}{2016^{2017}+1}\)
B=\(\frac{2016^{2017}-3}{2016^{2018}-3}\)
B=\(\frac{2016^{2017}-3}{2016^{2018}-3}\)<1 nên B<\(\frac{2016^{2017}-3+2019}{2016^{2018}-3+2019}\)=\(\frac{2016^{2017}+2016}{2016^{2018}+2016}\)=\(\frac{2016\left(2016^{2016}+1\right)}{2016\left(2016^{2017}+1\right)}\)=\(\frac{2016^{2016}+1}{2016^{2017}+1}\)=A
Vậy A>B
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