1,so sánh A và B biết:A=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2010};B=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{17}\)
Những câu hỏi liên quan
So sánh P và Q, biết: \(P=\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}\) và \(Q=\dfrac{2010+2011+2012}{2011+2012+2013}\)
\(Q=\dfrac{2010+2011+2012}{2011+2012+2013}=\dfrac{2010}{2011+2012+2013}+\dfrac{2011}{2011+2012+2013}+\dfrac{2012}{2011+2012+2013}\)
Ta có: \(\dfrac{2010}{2011+2012+2013}< \dfrac{2010}{2011}\)
\(\dfrac{2011}{2011+2012+2013}< \dfrac{2011}{2012}\)
\(\dfrac{2012}{2011< 2012< 2013}< \dfrac{2012}{2013}\)
\(\Rightarrow\dfrac{2010}{2011+2012+2013}+\dfrac{2011}{2011+2012+2013}+\dfrac{2012}{2011+2012+2013}\)
\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}\)
\(P>Q\)
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\(\dfrac{1}{1+\dfrac{2010}{2011}+\dfrac{2010}{2012}}+\dfrac{1}{1+\dfrac{2011}{2010}+\dfrac{2011}{2012}}+\dfrac{1}{1+\dfrac{2012}{2011}+\dfrac{2012}{2010}}\) và \(\dfrac{2016}{2017}\)
so sánh \(\dfrac{1}{1+\dfrac{2010}{2011}+\dfrac{2010}{2012}}+\dfrac{1}{1+\dfrac{2011}{2010}+\dfrac{2011}{2012}}+\dfrac{1}{1+\dfrac{2012}{2011}+\dfrac{2012}{2010}}\)và \(\dfrac{2016}{2017}\) giúp mik với
So sánh:
A=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}\) và B= \(\dfrac{2010+2011}{2011+2012}\)
Ta có:
\(A=\dfrac{2010}{2011}+\dfrac{2011}{2012}\)
\(B=\dfrac{2010+2011}{2011+2012}\)
\(=\dfrac{2010}{2011+2012}+\dfrac{2011}{2011+2012}\)
Áp dụng tính chất \(\dfrac{a}{b}>\dfrac{a}{b+m}\) ta có:
\(\left\{{}\begin{matrix}\dfrac{2010}{2011}>\dfrac{2010}{2011+2012}\\\dfrac{2011}{2012}>\dfrac{2011}{2011+2012}\end{matrix}\right.\)
\(\Rightarrow\dfrac{2010}{2011}+\dfrac{2011}{2012}>\dfrac{2010}{2011+2012}+\dfrac{2011}{2011+2012}\)
Hay \(\dfrac{2010}{2011}+\dfrac{2011}{2012}>\dfrac{2010+2011}{2011+2012}\)
Vậy \(A>B\)
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So sánh P và Q
\(P=\dfrac{2010}{2011}+\dfrac{2010}{2012}+\dfrac{2012}{2013};Q=\dfrac{2010+2011+2012}{2011+2012+2013}\)
\(Q=\dfrac{2010+2011+2012}{2011+2012+2013}=\dfrac{2010}{2011+2012+2013}+\dfrac{2011}{2011+2012+2013}+\dfrac{2012}{2011+2012+2013}\)Ta thấy:
\(\dfrac{2010}{2011}>\dfrac{2010}{2011+2012+2013}\\ \dfrac{2011}{2012}>\dfrac{2011}{2011+2012+2013}\\ \dfrac{2012}{2013}>\dfrac{2012}{2011+2012+2013}\\ \Rightarrow\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}>\dfrac{2010}{2011+2012+2013}+\dfrac{2011}{2011+2012+2013}+\dfrac{2012}{2011+2012+2013}\\ \Leftrightarrow P>Q\)
Vậy \(P>Q\)
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1,
a,tính:\(\dfrac{\dfrac{7}{2012}+\dfrac{7}{9}-\dfrac{1}{4}}{\dfrac{5}{9}-\dfrac{1}{2012}-\dfrac{1}{2}}\)
b,so sánh:A=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2010};B=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{17}\)
\(\dfrac{m+2009}{m+2011}\)và\(\dfrac{m+2010}{m+2012}\)hãy so sánh hai số đấy
Cho A=\(\dfrac{2010^{2011+1}}{2010^{2012+1}}\)và B=\(\dfrac{2010^{2010+1}}{2010^{2011+1}}\)
so sánh A và B
\(2010A=\dfrac{2010^{2012}+2010}{2010^{2012}+1}=1+\dfrac{2009}{2010^{2012}+1}\)
\(2010B=\dfrac{2010^{2011}+2010}{2010^{2011}+1}=1+\dfrac{2009}{2010^{2011}+1}\)
mà \(2010^{2012}+1>2010^{2011}+1\)
nên A<B
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So sánh A và B:
1. Adfrac{79^{2011} - 5}{79^{2011} + 8} và Bdfrac{79^{2012} - 6}{79^{2011} + 7}
2. Adfrac{43}{2011^{2012}}+dfrac{79}{2011^{2013}} và Bdfrac{79}{2011^{2012}}+dfrac{43}{2011^{2013}}
3. Adfrac{2010}{2011}:dfrac{2011}{2012} và Bdfrac{2010+2011}{2011+2012}
4. Adfrac{n}{2n+1} và Bdfrac{3n+1}{6n+3}
Thanks mấy bạn trước nha!!
Đọc tiếp
So sánh A và B:
1. A=\(\dfrac{79^{2011} - 5}{79^{2011} + 8}\) và B=\(\dfrac{79^{2012} - 6}{79^{2011} + 7}\)
2. A=\(\dfrac{43}{2011^{2012}}\)+\(\dfrac{79}{2011^{2013}}\) và B=\(\dfrac{79}{2011^{2012}}\)+\(\dfrac{43}{2011^{2013}}\)
3. A=\(\dfrac{2010}{2011}\):\(\dfrac{2011}{2012}\) và B=\(\dfrac{2010+2011}{2011+2012}\)
4. A=\(\dfrac{n}{2n+1}\) và B=\(\dfrac{3n+1}{6n+3}\)
Thanks mấy bạn trước nha!!
2.A=\(\dfrac{43.11}{2011^{2013}}\)+\(\dfrac{79}{2011^{2013}}\)=\(\dfrac{43.11+79}{2011^{2013}}\)
B=\(\dfrac{79.11}{2011^{2013}}\)+\(\dfrac{43}{2011^{2013}}\)=\(\dfrac{79.11+43}{2011^{2013}}\)
Ta có: 43.11+79=43.(10+1)+79=43.10+43+79=430+122
79.11+43=79.(10+1)+43=79.10+79+43=790+122
Vì 430+122<790+122 nên 43.11+79<79.11+43 (1)
Mà 20112013<20112013 (2)
Từ (1) và (2) suy ra A<B
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3. A=\(\dfrac{2010.2012}{2011.2011}\)
Vì B<1 nên B>\(\dfrac{2010}{2012}\)=\(\dfrac{2010.2012}{2012.2012}\)
Vì 2010.2012=2010.2012; 2011.2011<2012.2012 nên B>A
4. A=\(\dfrac{3n}{3\left(2n+1\right)}\)=\(\dfrac{3n}{6n+3}\)
Vì 6n+3=6n+3; 3n<3n+1 nên A<B
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