Question

so sánh

\(\dfrac{2003}{2004}+\dfrac{2004}{2005}\) và \(\dfrac{2003+2004}{2004+2005}\)

Answer 1

Cho A=\(\dfrac{2003}{2004}\)+\(\dfrac{2004}{2005}\); B=\(\dfrac{2003+2004}{2004+2005}\)

Ta có: B=\(\dfrac{2003}{2004+2005}\)+\(\dfrac{2004}{2004+2005}\)

Vì: \(\dfrac{2003}{2004+2005}< \dfrac{2003}{2004}\)

\(\dfrac{2004}{2004+2005}< \dfrac{2004}{2005}\)

=>\(\dfrac{2003}{2004+2005}+\dfrac{2004}{2004+2004}< \dfrac{2003}{2004}+\dfrac{2004}{2005}\)

=>\(\dfrac{2003+2004}{2004+2005}< \dfrac{2003}{2004}+\dfrac{2004}{2005}\)

=>B<A

Vậy B<A