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\(N=\frac{2004+2005}{2005+2006}=\frac{2004}{2005+2006}+\frac{2005}{2005+2006}\)
\(\text{Vì }\frac{2004}{2005}>\frac{2004}{2005+2006};\frac{2005}{2006}>\frac{2005}{2005+2006}\text{nên:}\)
\(\frac{2004}{2005}+\frac{2005}{2006}>\frac{2004}{2005+2006}+\frac{2005}{2005+2006}\)
Vậy M>N
\(M=\frac{2004}{2005}+\frac{2005}{2006}\)
\(\Rightarrow M>\frac{2004}{2006+2005}+\frac{2005}{2005+2006}\)
\(\Rightarrow M>\frac{2004+2005}{2005+2006}=N\)
\(\Rightarrow M>N\)
Ta thấy :
2004/2005 >2004/2005+2006
2005/2006> 2005/2005+2006
=> 2004/2005 + 2005/2006 >2004+2005 / 2005+2006
Ta có: \(\frac{2004}{2005}>\frac{2004}{2005+2006}\) (1)
\(\frac{2005}{2006}>\frac{2005}{2005+2006}\) (2)
Từ (1) và (2) => \(\frac{2004}{2005}+\frac{2005}{2006}>\frac{2004+2005}{2005+2006}\) => M>N
Ai k mik mik k lại. chúc các bạn thi tốt
\(A=\frac{2005^{2005}+1}{2005^{2006}+1}\)
\(2005A=\frac{2005^{2006}+2005}{2005^{2006}+1}=\frac{2005^{2006}+1+2004}{2005^{2006}+1}=\frac{2005^{2006}+1}{2005^{2006}+1}+\frac{2004}{2005^{2006}+1}\)
\(B=\frac{2005^{2004}+1}{2005^{2005}+1}\)
\(2005B=\frac{2005^{2005}+2005}{2005^{2005}+1}=\frac{2005^{2005}+1+2004}{2005^{2005}+1}=\frac{2005^{2005}+1}{2005^{2005}+1}+\frac{2004}{2005^{2005}+1}\)
Vì \(\frac{2004}{2005^{2006}+1}
