3. (5 points) If $\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}<\frac{x}{2}$, then the minimum value of the natural number $x$ is
【Solution】Solution: $\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\frac{77}{30} \approx 2.6
\end{array}
$$

Since $x$ is a natural number, the smallest value of $x$ is 3.
Answer: The smallest value of the natural number $x$ is 3.
Therefore, the answer is: 3.