Question

[Cấn Thuỵ An]

\(A=\frac{2005^{2005}+1}{2005^{2006}+1}\)VÀ \(B=\frac{2005^{2004}+1}{2005^{2005}+1}\)

Hãy so sánh hai phân số trên

Answer 1

[Katherine Lilly Filbert]

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

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

Ta có: \(\frac{2005^{2005}+1+2004}{2005^{2006}+1+2004}=\frac{2005^{2005}+2005}{2005^{2006}+2005}=\frac{2005\left(2005^{2004}+1\right)}{2005\left(2005^{2005}+1\right)}=\frac{2005^{2004}+1}{2005^{2005}+1}\)

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

=> A < B