Question

n(n-1)!+(n+1)!+(n-1)!=kn(n)!(1+1/n)2

Answer 1

Solución:

n(n - 1)! + (n + 1)! + (n - 1)! = kn(n)!(1 + 1 / n)²
n(n - 1)! + (n + 1)n(n - 1)! + (n - 1)! = kn(n)(n - 1)!((n + 1) / n)²
n + (n + 1)n + 1 = kn(n)((n + 1) / n)²
n + n² + n + 1 = kn²(n + 1)² / n²
n² + 2n + 1 = k(n + 1)² 
(n + 1)² = k(n + 1)²
1 = k

k = 1