The series given is:

$5 + 0.5 + 0.05 + 0.005 + \dots$

This is a geometric series where the first term $a = 5$ and the common ratio $r = 0.1$ (since each term is multiplied by 0.1 to get the next term).

The sum $S$ of an infinite geometric series can be calculated using the formula:

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

provided that $|r| < 1$. In this case, $r = 0.1$, which satisfies $|r| < 1$, so we can use the formula.

Substitute the values of $a$ and $r$:

$S = \frac{5}{1 - 0.1} = \frac{5}{0.9} = \frac{50}{9}$

Thus, the sum of the convergent series is:

$S = \frac{50}{9} \approx 5.56$

Would you like further details or clarification?

Related Questions:

1. What is the general formula for the sum of a geometric series?
2. How do we determine if a geometric series converges or diverges?
3. Can a geometric series converge if $|r| \geq 1$?
4. What are some real-life applications of converging geometric series?
5. How do you find the sum of a finite geometric series?

Tip: When solving geometric series problems, always check that the absolute value of the common ratio is less than 1 for convergence.