Cho A=1/2^2+1/3^2+1/4^2+1/5^2+1/6^2+…+1/49^2+1/50^2 So sánh A với 1

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1. `A = 1/2^2 + 1/3^2 + 1/4^2 + … + 1/50^2 `

   `A = 1/(2.2) + 1/(3.3) + 1/(4.4) + …. + 1/(50.50) < 1/(1.2) + 1/(2.3) + 1/(3.4) + … + 1/(49.50)`

   `A = 1/(2.2) + 1/(3.3) + 1/(4.4) + …. + 1/(50.50) < 1/1 – 1/2 + 1/2 – 1/3 + …. + 1/49 – 1/50`

   `A = 1/(2.2) + 1/(3.3) + 1/(4.4) + …. + 1/(50.50) < 1/1 – 1/50`

   `A = 1/(2.2) + 1/(3.3) + 1/(4.4) + …. + 1/(50.50) < 49/50`

   Mà ` A < 49/50 ; 49/50 < 1 ⇒ A < 1`

   Vậy , `A < 1`

    

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