Tính tổng A A = 1. 3^2 + 3.5^2 + 5.7^2 +….+ 97.99^2 Mong các bạn giúp nhaaaaa !!! Cảm mownnn ! Hứa vote luôn !!!

`A = 1. 3^2 + 3. 5^2 + 5. 7^2 + … + 97. 99^2`

`= 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 – 2. 1. 3 + 3. 5. 7 – 2. 3. 5 + 5. 7. 9 – 2. 5. 7 + … + 97. 99. 101 – 2. 97. 99`

`= (1. 3. 5 + 3. 5. 7 + 5. 7. 9 + … + 97. 99. 101) – (2. 1. 3 + 2. 3.5 + 2. 5. 7 + … + 2. 97. 99)`

`= (1. 3. 5 + 3. 5. 7 + 5. 7. 9+ … + 97. 99. 101) – 2. (1.3 + 3.5 + 5.7 + … + 97. 99)`

Gọi `M = 1. 3. 5 + 3. 5. 7 + 5. 7. 9 + … + 97. 99. 101, N = 2. (1.3 + 3.5 + 5.7 + … + 97. 99)`

`=> A = M – N`

`+) => 8M = 1. 3. 5. 8 + 3. 5. 7. 8 + 5. 7. 9. 8 + … + 97. 99. 101. 8`

 `=> 8M = 1. 3. 5. (7 + 1) + 3. 5. 7. (9 – 1) + 5. 7. 9. (11 – 3) + … + 97. 99. 101. (103 – 95)`

`=> 8M = 1. 3. 5. 7 + 1. 3. 5 + 3. 5. 7. 9 – 1. 3. 5. 7 + 5. 7. 9. 11 – 3. 5. 7. 9 + … + 97. 99. 101. 103 – 95. 97. 99. 101`

`=> 8M = 1. 3. 5 + 97. 99. 101. 103`

`=> 8M = 15 + 99900009`

`=> 8M = 99900024`

`=> M = 99900024 : 8 = 12487503`

`+) => 3N = 6. (1. 3 + 3. 5 + 5. 7 + … + 97. 99)`

`=> 3N = 1. 3. 6 + 3. 5. 6 + 5. 7. 6 + … + 97. 99. 6`

`=> 3N = 1. 3. (5 + 1) + 3. 5. (7 – 1) + 5. 7. (9 – 3) + … + 97. 99. (101 – 95)`

`=> 3N = 1. 3 + 1. 3. 5 + 3. 5. 7 – 1. 3. 5 + 5. 7. 9 – 3. 5. 7 + … + 97. 99. 101 – 95. 97. 99`

`=> 3N = 1. 3 + 97. 99. 101`

`=> 3N = 3 + 969903`

`=> 3N = 969906`

`=> N = 969906 : 3 = 323302`

`=> A = M – N = 12487503 – 323302 = 12164201`

Vậy `A = 12164201`