Question

[Chí]

CMR: 1/5²+1/6²+1/7²+...+1/2007² lớn hơn 1/5

Answer 1

[nghia]

\(\frac{1}{5^2}+\frac{1}{6^2}+......+\frac{1}{2007^2}>\frac{1}{5}\)

Có \(\frac{1}{5^2}>\frac{1}{4.5}\)

    \(\frac{1}{6^2}>\frac{1}{5.6}\)

     \(........\)

     \(\frac{1}{2007^2}=\frac{1}{2006.2007}\)

\(\Rightarrow\frac{1}{5^2}+\frac{1}{6^2}+.......+\frac{1}{2007^2}< \frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{2006.2007}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{2006}-\frac{1}{2007}\)

\(=\frac{1}{4}-\frac{1}{2007}\)

\(=\frac{2003}{8028}>\frac{1}{5}\)