Đáp án:

`I= 1.3.3 + 3.5.5 + 5.7.7 + ... + 97.99.99`

`= 1.3(5 – 2) + 3.5(7 – 2) + 5.7(9 – 2) + ... + 97.99(101 – 2)`

`= (1.3.5 – 1.3.2) + (3.5.7 – 3.5.2) + (5.7.9 – 5.7.2) + ... + (97.99.101 – 97.99.2)`

`= (1.3.5 + 3.5.7 + 5.7.9 + ... + 97.99.101) – 2(1.3 + 3.5 + 5.7 + ... + 97.99)`

Đặt `M = 1.3.5 + 3.5.7 + 5.7.9 + ... + 97.99.101`

       `N = 1.3 + 3.5 + 5.7 + ... + 97.99`

`8M = 1.3.5.8 + 3.5.7.(9 – 1) + 5.7.9.(11 – 3) + ... + 97.99.101.(103 – 95)`

`= 1.3.5.8 + (3.5.7.9 – 1.3.5.7) + (5.7.9.11 – 3.5.7.9) + ... + (97.99.101.103 – 95.97.99.101)`

`= 1.3.5.8 – 1.3.5.7 + 97.99.101.103`

`= 1.3.5.(8 – 7) + 97.99.101.103`

`= 15 + 97.99.101.103`

`⇒M=(15 + 97.99.101.103)/8 (1)`

` 6N = 1.3.6 + 3.5.6 + 5.7.6 + ... + 97.99.6`

`= 1.3.(5 + 1) + 3.5.(7 – 1) + 5.7.(9 – 3) + ... + 97.99.(101 – 95)`

`= 1.3.5 + 1.3.1 + 3.5.7 – 3.5.1 + 5.7.9 – 5.7.3 + ... + 97.99.101 – 97.99.95`

`= 1.3.1 + 97.99.101`

`= 3 + 97.99.101`

`⇒N=(3 + 97.99.101)/6 (2)`

Từ `(1)(2)⇒I=M+2N=(15 + 97.99.101.103)/8+2 (3 + 97.99.101)/6`

`=(15 + 97.99.101.103-8-8.97.33.101)/8`

`=(7+97.33.101.301)/8`

`=12 164 201`

`⇒I=12 164 201`