(x_n+1)^n=\sum_{k=0}^n {n \choose k} x_n^k = 1+{n \choose 1}x_n+ {n\choose 2}x_n^2+{n\choose 3}x_n^3+\cdots + {n\choose n}x_n^n > {n \choose 3} x_n^3=\frac{n!}{3!(n-3)!}x_n^3