Cmr `1-1/2^2-1/3^2-1/4^2-….-1/2006^2>1/2006`

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1. Bài làm :

   *Sai lớp !

   Giải :

   Đặt `A = 1 – 1/(2^2) – 1/(3^2) – 1/(4^2) – … – 1/(2006^2)`

   `→ A = 1 – ( 1/(2^2) – 1/(3^2) – 1/(4^2) – … – 1/(2006^2) )`

   `→ A > 1 – 1/(1.2) – 1/(2.3) – 1/(3.4) – … – 1/(2005.2006)`

   `→ A > 1 – ( 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/(2005) – 1/(2006) )`

   `→ A > 1 – ( 1 – 1/(2006) )`

   `→ A > 1/(2006) →` đpcm .

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2. `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2} > 1/2006`

   `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2}`

   `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2} > ` `(1/{1xx2} + 1/{2xx3} + 1/{3xx4} + … + 1/{2005xx2006}`

   `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2} > ` `(1-1/2+1/2-1/3+1/3-1/4 + …+1/2005-1/2006`

   `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2} > ` `(1-0-2006)`

   `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2} > ` `(1-2006)`

   `1-1/{2^2} – 1/{3^2} – 1/{4^2} – … – 1/{2006^2} > ` `1/2006` `(Đpcm)`

    

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