Bonjour,
1) A(1) = (2x1 - 1)² - 1x(3x1 - 2) = 1² - 1 = 0
...
A(5) = (2x5 - 1)² - 5x(3x5 - 2) = 9² - 65 = 16 = 4² = (5 - 1)²
A(10) = (2x10 - 1)² - 10x(3x10 - 2) = 19² - 280 = 81 = 9² = (10 - 1)²
On peut conjecturer que A(n) = (n - 1)²
2) A(n) = (2n - 1)² - n(3n - 2)
= 4n² - 4n + 1 -3n² + 2n
= n² -2n + 1
= (n - 1)²
