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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
\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)
\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)
\(=\frac{2011}{2011}-\frac{1999}{1999}\)
\(=1-1=0\)
\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)
\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)
\(=\frac{2011}{2011}-\frac{1999}{1999}\)
\(=1-1=0\)
\(\frac{2010}{2011}\)> \(\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}\)> \(\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}\)> \(\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}\)+ \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)> \(\frac{2010+2011+2012}{2011+2012+2013}\)
=> P > Q
\(\frac{1999}{2011}-\frac{2011}{1999}-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)
\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)
\(=\left(\frac{1999}{2011}+\frac{12}{2011}\right)-\frac{2011}{1999}+\frac{12}{1999}\)
\(=1-\left(\frac{2011}{1999}-\frac{12}{1999}\right)\)
\(=1-1\)
\(=0\)
NHÉ !!!!!!!
Ta có : \(\frac{1999}{2011}-\frac{2011}{1999}-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)
=\(\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)
=\(\left(\frac{1999}{2011}+\frac{12}{2011}\right)+\left(\frac{12}{1999}-\frac{2011}{1999}\right)\)
=1-1
=0
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??????????
