The image you uploaded appears to contain a mathematical series:

$\frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \dots$

This is an infinite geometric series of the form:

$S = \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \dots$

To find the sum of this series, we recognize that it has the first term $a = \frac{1}{x}$ and the common ratio $r = \frac{1}{x}$, assuming $|r| < 1$, i.e., $|x| > 1$.

The sum of an infinite geometric series is given by the formula:

$S = \frac{a}{1 - r}$

Substituting $a = \frac{1}{x}$ and $r = \frac{1}{x}$, we get:

$S = \frac{\frac{1}{x}}{1 - \frac{1}{x}} = \frac{\frac{1}{x}}{\frac{x-1}{x}} = \frac{1}{x-1}$

Thus, the sum of the series is:

$S = \frac{1}{x - 1} \quad \text{for} \quad |x| > 1$

Would you like more details on geometric series, or any other questions about this result?

Here are 5 related questions:

1. How can you derive the sum formula for an infinite geometric series?
2. What happens if $|x| \leq 1$ in this series?
3. Can this series be applied in real-world problems, such as finance or physics?
4. How do we generalize geometric series for complex numbers?
5. What is the importance of convergence in infinite series?

Tip: Always check the conditions for convergence before summing an infinite series to ensure that the sum formula is applicable.