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Question

So sánh: $A=\frac{2005^{2005}+1}{2005^{2006}+1};B=\frac{2005^{2004}+1}{2005^{2005}+1}$

Hoàng Phương Mai · Accepted Answer

$A=\frac{2005^{2005}+1}{2005^{2006}+1}$$\Rightarrow2005A=\frac{2005^{2006}+2005}{2005^{2006}+1}$$\Rightarrow2005A=1+\frac{2004}{2005^{2006}+1}$$B=\frac{2005^{2004}+1}{2005^{2005}+1}$$\Rightarrow2005B=\frac{2005^{2005}+2005}{2005^{2005}+1}$$\Rightarrow2005B=1+\frac{2004}{2005^{2005}+1}$Ta thấy $\frac{2004}{2005^{2005}+1}>\frac{2004}{2005^{2006}+1}$Suy ra $1+\frac{2004}{2005^{2005}+1}>1+\frac{2004}{2005^{2006}+1}$hay 2005B>2005AVậy B>ACâu trả lời: $A=\frac{2005^{2005}+1}{2005^{2006}+1}$$\Rightarrow2005A=\frac{2005^{2006}+2005}{2005^{2006}+1}$$\Rightarrow2005A=1+\frac{2004}{2005^{2006}+1}$$B=\frac{2005^{2004}+1}{2005^{2005}+1}$$\Rightarrow2005B=\frac{2005^{2005}+2005}{2005^{2005}+1}$$\Rightarrow2005B=1+\frac{2004}{2005^{2005}+1}$Ta thấy $\frac{2004}{2005^{2005}+1}>\frac{2004}{2005^{2006}+1}$Suy ra $1+\frac{2004}{2005^{2005}+1}>1+\frac{2004}{2005^{2006}+1}$hay 2005B>2005AVậy B>A

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