Find the sum of the series: \(\sum_{n=1}^{\infty} \frac{x^n}{\sqrt{n+2}}\)

Analysis:

The question asks to find the sum of the given series. However, the image only shows the series itself and the word 'Най(', which likely means 'Find' in Russian. Without a specific instruction on what to 'find' (e.g., the radius of convergence, the interval of convergence, or if it's a known series whose sum can be determined), it's impossible to provide a definitive answer for the sum of the series in a closed form. This type of series is generally related to power series and their convergence properties.

To provide a complete solution, one would typically:

1. Determine the radius of convergence using the Ratio Test or Root Test.
2. Test the endpoints of the interval of convergence.
3. If possible, relate the series to a known Maclaurin or Taylor series expansion of a function.

Given the limited information and the ambiguity of the task (only 'Find' is implied), a step-by-step solution for the sum itself cannot be provided without further clarification or context.

The problem as presented is incomplete and requires further specification.