Given number:
$$7^{n + 1} \cdot 8^{- n}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = 7^{n + 1}$$
and
$$x_{0} = -8$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-8 + \lim_{n \to \infty}\left(7^{- n - 2} \cdot 7^{n + 1}\right)\right)$$
Let's take the limitwe find
False
False
$$R = 0$$