The power series is given in the form $\sum_{n=0}^{\infty} x^{n}$ and $\sum_{n=0}^{\infty}\left(\frac{x}{5}\right)^{n}$, which converges for $|x|<1$ and $|\frac{x}{5}|<1$ respectively. This means that $x$ must be between $-1$ and $1$ and $x$ must be between $-5$
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