Answer
False
Work Step by Step
Ratio Test: Let us consider a series $\Sigma a_k$ whose limit $l$ can be obtained as: $ l=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|$
1. For $l \lt 1$, the series is absolutely convergent.
2. For $l \gt 1$, the series is divergent.
3. For $l = 1$, the series is inconclusive.
Therefore, $ L=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|\\=\lim\limits_{k \to \infty} \dfrac{x^{k+1}}{(k+1)!} \times \dfrac{x^k}{(k+1)!} \\=\lim\limits_{k \to \infty} \dfrac{x}{k+1} \\=0$
So, we can conclude that the given series converges absolutely for all $x$ when $l \lt 1$.
Therefore, the given statement is false.
