Question

a=\(\frac{2005^{2005}+1}{2005^{2006}+1}\) va b=\(\frac{2005^{2004}+1}{2005^{2005}+1}\)

                    so sánh a và b

Answer 1

 \(2005a=\frac{2005^{2006}+2005}{2005^{2006}+1}=\frac{2005^{2006}+1}{2005^{2006}+1}+\frac{2004}{2005^{2006}+1}=1+\frac{2004}{2005^{2006}+1}\)

\(2005b=\frac{2005^{2005}+2005}{2005^{2005}+1}=\frac{2005^{2005}+1}{2005^{2005}+1}+\frac{2004}{2005^{2005}+1}=1+\frac{2004}{2005^{2005}+1}\)

Ta thấy :\(2005^{2006}+1>2005^{2005}+1\)

\(\Rightarrow\frac{2004}{2005^{2006}+1}< \frac{2004}{2005^{2005}+1}\)

\(\Rightarrow1+\frac{2004}{2005^{2006}+1}< 1+\frac{2004}{2005^{2005}+1}\)

\(\Rightarrow2005a< 2005b\)

\(\Rightarrow a< b\)

Answer 2

\(A< \frac{2005^{2005}+1+2004}{2005^{2006}+1+2004}=\frac{2005^{2005}+2005}{2005^{2006}+2005}=\frac{2005\left(2005^{2004}+1\right)}{2005\left(2005^{2005}+1\right)}=\frac{2005^{2004}+1}{2005^{2005}+1}=B\)

Vậy A < B