Đáp án:
Bài 7:
Ta có:
`M = (1 + 1/2 + 1/3 + 1/4 + ................. + 1/2018) . 2 . 3 . 4 ........2018`
`M =[ (1 + 1/2018) + (1/2 +1/2017) + (1/3 + 1/2016) + .................. +(1/1009 + 1/1010)] . 2 . 3 . 4 . .... 2018`
`M=[ 2019/2018+ 2019/(2.2017) + 2019/(3 . 2016) + ....... + 2009/(1009.1010) ] . 2 . 3 .4 ... 2018`
`M =( 1/2018 + 1/(2.2017) + 1/( 3 . 2016) + ............. + 1/(1009 . 1010) ) . 2019 . 2 . 3 . 4 ... 2018 ⋮ 2019`
Bài 8:
Bạn ghi sai đề nên mình sửa
`A = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256`
`2A = 2 . (1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256)`
`2A = 1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32 + 1/64 - 1/128`
`2A + A = (1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32 + 1/64 - 1/128) +(1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256)`
`2A + A = 1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32 + 1/64 - 1/128 + 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256`
`3A = 1 - (1/2 - 1/2) + (1/4 - 1/4) - (1/8 - 1/8) + ............ + (1/64 - 1/64) - (1/128 - 1/128) - 1/256`
`3A = 1 - 1/256 < 1`
`⇒ A < 1/3`
`text{ @toanisthebest}`
