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$$ \lim_{n \to \infty} \left|\frac{a_{n+1}} {a_n} \right| = \lim_{n\to \infty} \left|\frac {(n+1)!x^{n+1} {n!x^n} \right| = \lim_{n \to \infty} (n+1) |x| = \infty $$