Giúp em những câu có chữ VN với T-T

Bài 15:

`M = 1.2 + 2.3 + 3.4 + ... + 109.110`

`3M = 1.2.3 + 2.3.3 + 3.4.3 + ... + 109.110.3`

`3M = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... + 109.110.(111-108)`

`3M = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 109.110.111 - 108.109.110`

`3M = 109.110.111`

`M = (109 * 110 * 111) / 3`

`M = 443830`

`N = 1.2.3 + 2.3.4 + 3.4.5 + ... + 98.99.100`

`4N = 1.2.3.(4-0) + 2.3.4.(5-1) + ... + 98.99.100.(101-97)`

`4N = 1.2.3.4 - 0.1.2.3 + 2.3.4.5 - 1.2.3.4 + ... + 98.99.100.101 - 97.98.99.100`

`4N = 98.99.100.101`

`N = (98 * 99 * 100 * 101) / 4`

`N = 24497550`

Bài 16:

`G = 1.3 + 2.4 + 3.5 + ... + 98.100`

`G = 1.(2+1) + 2.(3+1) + 3.(4+1) + ... + 98.(99+1)`

`G = (1.2 + 1) + (2.3 + 2) + (3.4 + 3) + ... + (98.99 + 98)`

`G = (1.2 + 2.3 + 3.4 + ... + 98.99) + (1 + 2 + 3 + ... + 98)`

Đặt `M' = 1.2 + 2.3 + ... + 98.99`

`3M' = 98.99.100 => M' = 323400`

Đặt `S = 1 + 2 + ... + 98`

`S = (98+1)*98 / 2 = 4851`

`G = M' + S = 323400 + 4851 = 328251`

Bài 17:

`H = 1.4 + 2.5 + 3.6 + ... + 99.102`

`H = 1.(2+2) + 2.(3+2) + ... + 99.(100+2)`

`H = (1.2 + 2.1) + (2.3 + 2.2) + ... + (99.100 + 99.2)`

`H = (1.2 + 2.3 + ... + 99.100) + 2(1 + 2 + ... + 99)`

Đặt `M'' = 1.2 + 2.3 + ... + 99.100`

`3M'' = 99.100.101 => M'' = 333300`

Đặt `S' = 1 + 2 + ... + 99`

`S' = (99+1)*99 / 2 = 4950`

`H = M'' + 2S' = 333300 + 2*4950 = 333300 + 9900 = 343200`

Bài 18:
`a)`
Ta có:

`A = 199 . 201 = (200 - 1)(200 + 1) = 200.200 - 1`

`B = 200 . 200`

Vì `200.200 - 1 < 200.200` nên `A < B`

`b)`

Ta có:

`D = 134 . 136 + 12 = (135 - 1)(135 + 1) + 12 = 135.135 - 1 + 12 = 135.135 + 11`

`B = 135 . 135 + 16`

Vì `11 < 16` nên `135.135 + 11 < 135.135 + 16`

Vậy `D < B`

`c)`

Ta có:

`C = 12341234 . 4567 = (1234 * 10001) . 4567 = 1234 . 4567 . 10001`

`N = 45674567 . 123 = (4567 * 10001) . 123 = 4567 . 123 . 10001`

Vì `1234 > 123` nên `1234 . 4567 > 123 . 4567`

Vậy `C > N`