NP
4
K
Khách
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DH
1
TL
2
PM
20 tháng 3 2018
S= \(\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+2}{2011}\)
= 3 + \(\frac{2}{2011}-\frac{1}{2012}-\frac{1}{2013}\)
có \(\frac{1}{2011}>\frac{1}{2012}\)và \(\frac{1}{2011}>\frac{1}{2013}\)
\(\Rightarrow S>3\)
20 tháng 3 2019
AM-GM:\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2010}\ge4\sqrt[4]{\frac{2010.2011.2012.2013}{2011.2012.2013.2010}}=4\sqrt[4]{1}=4\)
\(\Rightarrow S\ge4\)
^^
LH
4
T
24 tháng 3 2018
Bài nãy sai rồi, cho mình làm lại nha:
\(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}=\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}\)
\(=1-\frac{1}{2012}+1-\frac{1}{2013}+1+\frac{1}{2011}\)
Vì: \(\frac{1}{2011}>\frac{1}{2012}>\frac{1}{2013}\Rightarrow\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2012}+\frac{1}{2012}>0\)
\(\Rightarrow\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}>3\)
Nên \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}>3\)
NM
17 tháng 3 2019
\(\frac{2010}{2011}\)> \(\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}\)> \(\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}\)> \(\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}\)+ \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)> \(\frac{2010+2011+2012}{2011+2012+2013}\)
=> P > Q
20 tháng 4 2016
P = \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
Q = \(\frac{2010+2011+2012}{2011+2012+2013}\) = \(\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Vì: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
P > Q
LT
1
21 tháng 3 2019
Ta có :
\(B=\frac{1011}{2012+2013}\)+\(\frac{2012}{2012+2013}\)=\(\frac{2011+2012}{2012+2013}\)
Vì:
\(\frac{2011}{2012+2013}\)<\(\frac{2011}{2012}\); \(\frac{2012}{2012+2013}< \frac{2012}{2013}\)
=> \(\frac{2011+2012}{2012+2013}< \frac{2011}{2012}+\frac{2012}{2013}\)
Mà \(\frac{2011+2012}{2012+2013}\)=B ; \(\frac{2011}{2012}+\frac{2012}{2013}\)
Vậy A <B
NN
2
24 tháng 3 2019
Ta có :
A=\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\left(1\right)\)
B=\(\frac{2011}{2012}+\frac{2012}{2013}\left(2\right)\)
Từ (1) và (2) suy ra A<B
24 tháng 3 2019
Đầu tiên:
Ta có:
B=\(\frac{2011}{2012+2013}\)+ \(\frac{2012}{2012+2013}\) = \(\frac{2011+2012}{2012+2013}\)
Vì:
\(\frac{2011}{2012+2013}\)< \(\frac{2011}{2012}\); \(\frac{2012}{2012+2013}\)< \(\frac{2012}{2013}\)
\(\Rightarrow\)\(\frac{2011+2012}{2012+2013}\)< \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)
Mà \(\frac{2011+2012}{2012+2013}\)= B; \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)
Vậy B>A
26 tháng 1 2016
bai thi .....................kho..........................kho..............troi.................thilanh.............................ret..................wa.........................dau................wa......................tich....................ung.....................ho.....................cho............do.................lanh
26 tháng 1 2016
bai thi .....................kho..........................kho..............troi.................thilanh.............................ret..................wa.........................dau................wa......................tich....................ung.....................ho.....................cho............do.................lanh...............tho...................bang..................mom...................thi...................nhu..................hut.....................thuoc................la.................lanh wa
S lớn hơn 3 vì , S = 3,000000741
Bài giải :
Theo đề bài ra ta có : n. (n - 1) : 2 = 435
=> n. (n - 1) = 435 . 2 = 870
=> n.(n-1) = 30. 29
Vậy n = 30.