Question

A= 1/2mũ2+1/3mu2+1/4mu2+...+1/2008mu2

Answer 1

\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+................+\dfrac{1}{2008^2}\)

Ta thấy :

\(\dfrac{1}{2^2}< \dfrac{1}{1.2}\)

\(\dfrac{1}{3^2}< \dfrac{1}{2.3}\)

...................

\(\dfrac{1}{2008^2}< \dfrac{1`}{2007.2008}\)

\(\Leftrightarrow A< \dfrac{1}{1.2}+\dfrac{1}{2.3}+............+\dfrac{1}{2007.2008}\)

\(\Leftrightarrow A< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+..........+\dfrac{1}{2007}-\dfrac{1}{2008}\)

\(\Leftrightarrow A< 1-\dfrac{1}{2008}< 1\)

\(\Leftrightarrow A< 1\rightarrowđpcm\)