Réponse :
exprimer Un-1 et Un+1 en fonction de n
1) Un = 6 n + 8
Un-1 = 6(n-1) + 8 = 6 n - 6 + 8 = 6 n + 2
Un+1 = 6(n+1) + 8 = 6 n + 6 + 8 = 6 n + 14
2) Un = n² - 2 n + 8
Un-1 = (n-1)²-2(n-1) + 8 = n²-2 n + 1 - 2 n + 2 + 8 = n² - 4 n + 11
Un+1 = (n+1)² - 2(n+1) + 8 = n²+ 2 n + 1 - 2 n - 2 + 8 = n² + 7
3) Un = n(n + 1)/(n+2)
Un-1 = (n-1)((n-1) + 1)/((n-1)+2) = n(n-1)/(n+1)
Un+1 = (n+1)(n+2)/(n+3)
4) Un = 5ⁿ
Un-1 = 5ⁿ⁻¹
Un+1 = 5ⁿ⁺¹
5) Un = (3ⁿ⁺¹)/2ⁿ
Un-1 = 3ⁿ/2ⁿ⁻¹
Un+1 = 3ⁿ⁺²/2ⁿ⁺¹
6) Un = (9 n - 5)/(4 n + 6)
Un-1 = (9(n-1) - 5)/(4(n-1) + 6) = (9 n - 14)/(4 n+2)
Un+1 = (9(n+1) - 5)/(4(n+1) + 6) = (9 n + 4)/(4 n+10)
7) Un = (n²/(n+1))ⁿ⁺¹
Un-1 = ((n-1)²/((n-1)+1))ⁿ⁻¹⁺¹ = ((n² - 2n + 1)/n)ⁿ
Un+1 = ((n+1)²/(n+1 +1))ⁿ⁺¹⁺¹ = (n²+2n+1)/(n+2))ⁿ⁺²
Explications étape par étape