Question

Chứng tỏ rằng B= 1-\(\dfrac{1}{2^2}-\dfrac{1}{3^2}-...-\dfrac{1}{2014^2}< \dfrac{1}{2004}\)

Ai LÀM KHÔNG

Answer 1

ta có \(1-\dfrac{1}{2^2}-..-\dfrac{1}{2014^2}=1-\left(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2014^2}\right)\)

\(\Rightarrow B< 1-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2013.2014}\right)\)

\(\Rightarrow B< 1-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2013}-\dfrac{1}{2014}\right)\)

\(\Rightarrow B< 1-\left(1-\dfrac{1}{2014}\right)=1-1+\dfrac{1}{2014}=\dfrac{1}{2014}\)

\(\Rightarrow B< \dfrac{1}{2014}\left(dpcm\right)\)

Answer 2

bài này hay nà