a)So sánh M và N bằng cách thuận tiện nhất
M=\(\frac{2010}{2011}\)+ \(\frac{2011}{2012}\) và N= \(\frac{2010+2011}{2011+2012}\)
b) So sánh P=\(\frac{2011\cdot2012-2}{2010\cdot2011+4020}\)
a,So sánh M và N bằng cách thuận tiện nhất
M = 2010/2011 + 2011/2012 và N = 2010 + 2011/2011+2012
b,So sánh P =2011 x 2012 - 2 / 2010x2011+4020
So sánh giá trị biểu thức bằng cách thuận tiện:
M = 2010/2011 + 2011/2012 và N = 2010+2011/2011+2012
Tìm cách thuận tiện nhất để so sánh M và N biết m = 2010 /2011 + 2011 / 2012 n bang 2010 +2011 /2011 + 2012
N=\(\frac{2010+2011}{2011+2012}=\frac{2010}{2011+2012}+\frac{2011}{2011+2012}\)
M=\(\frac{2010}{2011}+\frac{2011}{2012}\)
ta có \(\frac{2010}{2011+2012}< \frac{2010}{2011}\)
\(\frac{2011}{2011+2012}< \frac{2011}{2012}\)
-> N<M
So sánh A và B biết
A=\(\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}\)
B=\(\frac{2009+2010+2011}{2010+2011+2012}\)
A=2.998508205
B=0.999502735
suy ra A>B
Bài giải
Theo bài ra :
\(A=\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}\)
\(B=\frac{2009+2010+2011}{2010+2011+2012}=\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
Ta có :
\(\frac{2009}{2010}>\frac{2009}{2010+2011+2012}\)
\(\frac{2010}{2011}>\frac{2010}{2010+2011+2012}\)
\(\frac{2011}{2012}>\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}>\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }A>B\)
Bài giải
Theo bài ra :
\(A=\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}\)
\(B=\frac{2009+2010+2011}{2010+2011+2012}=\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
Ta có :
\(\frac{2009}{2010}>\frac{2009}{2010+2011+2012}\)
\(\frac{2010}{2011}>\frac{2010}{2010+2011+2012}\)
\(\frac{2011}{2012}>\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}>\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }A>B\)
So sánh
M= \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
N= \(\frac{2010+2011+2012}{2011+2012+2013}\)
N =\(\frac{2010+2011+2012}{2011+2012+2013}\)
\(\Rightarrow N=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Do: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013};\frac{2011}{2012}>\frac{2011}{2011+2012+2013};\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\Leftrightarrow N>M\)
CHO : \(A=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
VÀ : \(B=\frac{2010+2011+2012}{2011+2012+2013}\)
SO SÁNH A VÀ B
TA CÓ :
\(B=\frac{2010+2011+2012}{2011+2012+2013}\)
\(B=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
VÌ : \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
=> A > B
VẬY , A > B
Mình tự hỏi. sao banh biết rồi còn đăng lên làm gì??????????
So sánh : \(\frac{1}{1+\frac{2010}{2011}+\frac{2010}{2012}}+\frac{1}{1+\frac{2011}{2010}+\frac{2011}{2012}}+\frac{1}{1+\frac{2012}{2011}+\frac{2012}{2010}}\) và \(\frac{2016}{2017}\)
Ta có: \(\frac{1}{1+\frac{2010}{2011}+\frac{2010}{2012}}+\frac{1}{1+\frac{2011}{2010}+\frac{2011}{2012}}+\frac{1}{1+\frac{2012}{2011}+\frac{2012}{2010}}\)
\(=\frac{1}{2010\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}\right)}+\frac{1}{2011\left(\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2012}\right)}+\frac{1}{2012\left(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}\right)}\)
\(=\frac{\frac{1}{2010}}{\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}}+\frac{\frac{1}{2011}}{\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2012}}+\frac{\frac{1}{2012}}{\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}}\)
\(=\frac{\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}}{\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}}=1\)
Mà \(\frac{2016}{2017}< 1\)
Vậy \(\frac{1}{1+\frac{2010}{2011}+\frac{2010}{2012}}+\frac{1}{1+\frac{2011}{2010}+\frac{2011}{2012}}+\frac{1}{1+\frac{2012}{2010}+\frac{2012}{2011}}>\frac{2016}{2017}\)
dấu cần điền là : >
Vì kết quả của phép tính vế thứ 1 là 1
và phân số 2016/2017 bé hơn 1 nên ta điền dấu lớn
mình ko hiểu lắm sao tự nhiên lại đang \(\frac{1}{2010.\left[2010+2011+2012\right]}\)lại sang luôn \(\frac{\frac{1}{2010}}{2010+2011+2012}\)
so sánh P=\(\frac{2011\cdot2012-2}{2010\cdot2011+4020}\)với 1
Ta có: \(\frac{2011\times2012-2}{2010\times2011+4020}=\frac{2011\times\left(2010+2\right)-2}{2010\times2011+4020}=\frac{2011\times2010+4022-2}{2010\times2011+4020}=\frac{2011\times2010+4020}{2010\times2011+4020}=1\)
Vậy \(\frac{2011\times2012-2}{2010\times2011+4020}=1\)
\(P=\frac{2011.2012-2}{2010.2011+4020}=\frac{2010.2011+2.2011-2}{2010.2011+4020}=\frac{2010.2011+4042-2}{2010.2011+4020}=\frac{2010.2011+4040}{2010.2011+4040}=1\)
Vậy P = 1
M= \(\frac{2010}{2011}+\frac{2011}{2012}\)và N= \(\frac{2010+2011}{2011+2012}\)
SO SÁNH
\(M=\frac{2010}{2011}+\frac{2011}{2012}>\frac{2010}{2011+2012}+\frac{2011}{2011+2012}=\frac{2010+2011}{2011+2012}=N\)