Bài 9. Cho B = 1/4+ 1/9+ 1/16+⋯+ 1/81+ 1/100 . Chứng minh B > 65/132 Bài 10.Chứng minh (200-(3+ 2/3+ 2/4+ …+ 2/100))/(1/2+2/3+ 3/4+ …+ 99/100) = 2

Đáp án:

 Bài 9:

Ta có:

`B = 1/4 + 1/9 + 1/16 + ………… + 1/81 + 1/100`

`   =1/(2^2) + 1/(3^2) + 1/(4^2) + ……… +1/(9^2) + 1/(10^2)`

`⇔ B  > + 1/(2.3) + 1/(3.4) + ……… + 1/(9 . 10)+1/(9.11)`

`           =  1/2  + 1/2 – 1/3 + ………. +1/9 – 1/11`

`           =1/2 – 1/11 = 9/22`

Mà `9/22 = 99/132 > 65/132`

`⇒ B > 65/132`

bài 10: 

Ta có:

`( 200 – (3 + 2/3 + 2/4 +…………….+2/100))/(1/2 + 2/3 + 3/4 + ……….. +99/100)`

`= (200 – 2 + (2/2 + 2/3 + 2/4 + ………….. +2/100) )/( 1 – 1/2 + 1 – 1/3 + …… + 1 – 1/100)`

`=(198 – (2/2 + 2/3 + 2/4 + …………… + 2/100) )/( (1 + 1 + 1 + ………. +1) – (1/2 + 1/3 + 1/4 + …… +1/100) )`

`= (2 . ( 99 – ( 1/2 + 1/3 + 1/4 + ……………. + 1/100) ) )/( 99 – ( 1/2 + 1/3 + 1/4 + ……….. +1/100) )`

`=2/1 = 2`

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