a) `A= 1/14 . 84/(n+3) + 5/9 . 18/(2n+6)`
`A= 84/(14(n+3)) + 90/(9(2n+6))`
`A= 6/(n+3) + 10/(2n+6)`
`A= 12/(2n+6)+ 10/(2n+6)`
`A= (10+12)/(2n+6)`
`A= 22/(2n+6)`
`A= 22/(2(n+3)) = 11/(n+3)`
Vậy `A= 11/(n+3)`
b) Để A có giá trị là số nguyên
`=> 11` chia hết cho `n+3`
`=> n+3` ∈`Ư(11)= { 1; 11; -1; -11}`
`=> n ` ∈ `{ -3; 8; -4; -14}`
Vậy ` n ` ∈ `{ -3; 8; -4; -14}`
Câu 2:
`B= 3/2 + 3/2^2 + 3/2^3 +...+ 3/2^2018`
`1/2 B= 1/2( 3/2 + 3/2^2 + 3/2^3 +...+ 3/2^2018`
`1/2 B= 3/2^2 + 3/2^3 + 3/2^4+...+3/2^2019`
`B- 1/2 B = 3/2 + 3/2^2 + 3/2^3+...+3/2^2018 - 3/2^2 - 3/2^3 - ...-3/2^2018`
`1/2 B= 3/2 - 3/2^2018`
`B= (3/2 - 3/2^2018) : 1/2`
`B= (3/2 - 3/2^2018) .2`
`B = 3/2 . 2 - 3/2^2018 .2`
`B= 3 - 3/2^2017`
Vậy `B= 3- 3/2^2017`
