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Chứng minh A=1/1^2+1/2^2+1/3^2+...+1/50^2 < 2

Chứng minh :

A= 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<2

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Trả lời (1)

 
 
 
  • Ta có: \(\dfrac{1}{1^2}=1\)

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

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

    ..........

    \(\dfrac{1}{50^2}< \dfrac{1}{49.50}=\dfrac{1}{49}-\dfrac{1}{50}\)

    \(\Rightarrow A< 1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}=1+1-\dfrac{1}{50}=2-\dfrac{1}{50}< 2\)=> đpcm

      bởi Nguyễn Tiến 26/12/2018
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