montrer que (2n +1)² = 4 x n x (n+1) +1

(2n + 1)²
= 4n² + 4x + 1

4 x n x (n + 1) + 1
= 4n(n + 1) + 1
= 4n² + 4n + 1

(2n +1)² = (2n)² + 2 (2n) (1) + 1²
             = 4n² + 4n +1

4 x n x (n+1) +1  = 4n (n+1) +1
                         = 4n² + 4n +1

Donc (2n +1)² = 4 x n x (n+1) +1