Question

Chứng minh rằng : 

\(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{2013^2}+\dfrac{1}{2014^2}>\dfrac{1}{5}\)

Answer 1

Đặt \(A=\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{2014^2}\)

\(A>\dfrac{1}{5^2}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{2014.2015}\)

\(A>\dfrac{1}{5^2}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\)

\(A>\dfrac{1}{5^2}+\dfrac{1}{6}-\dfrac{1}{2015}\)

\(A>\dfrac{1}{5^2}+\dfrac{1}{6}-\dfrac{1}{150}=\dfrac{1}{5}\) (đpcm)

Answer 2

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