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`
`text{ @toanisthebest}`
