B= 2.3 + 3.4 + 4.5 + ... + 2018.2019

Đáp án:

`B = 2743390278`

Giải thích các bước giải:

`B = 2 . 3 + 3 . 4 + 4 . 5 + ... + 2018 . 2019`

`=> 3B = 3 . ( 2 . 3 + 3 . 4 + 4 . 5 + ... + 2018 . 2019 )`

`=> 3B = 2 . 3 . 3 + 3 . 4 . 3 + ... + 2018 . 2019 . 3`

`=> 3B = 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) + ... + 2018 . 2019 . ( 2020 - 2017 )`

`=> 3B = 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + ... + 2018 . 2019 . 2020 - 2017 . 2018 . 2019`

`=> 3B = - 1 . 2 . 3 + ( 2 . 3 . 4 - 2 . 3 . 4 ) + ... + ( 2017 . 2018 . 2019 - 2017 . 2018 . 2019 ) + 2018 . 2019 . 2020`

`=> 3B = - 6 + 2018 . 2019 . 2020`

`=> B = ( - 6 + 2018 . 2019 . 2020 )/3 `

`=> B = (-6)/3 + ( 2018 . 2019 . 2020)/3`

`=> B = - 2 + 2018 . 673 . 2020`

`=> B = 2743390280 - 2 = 2743390278`

Vậy `B = 2743390278`