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
Làm ơn hứa 5*
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
Làm ơn hứa 5*
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}`