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In the image, the statement is asking about a sequence \( (a_n)_{n \in \mathbb{N}} \) and its behavior as \( n \to +\infty \). Let's break it down:

1. \( L \in \mathbb{R} - \{0\} \) means that \( L \) is a real number and specifically not zero.
2. The condition given is:

   \[
   \lim_{n \to +\infty} \frac{a_n - L}{a_n + L} = 0.
   \]

3. Based on this condition, the question is asking to determine \( \lim_{n \to +\infty} a_n = \underline{\quad} \), i.e., the limit of the sequence \( a_n \) as \( n \to +\infty \).

### Solution Outline:

- The limit condition given implies that as \( n \to \infty \), the numerator \( a_n - L \) becomes very small compared to \( a_n + L \). This suggests that \( a_n \) approaches \( L \) because if \( a_n \to L \), then:

  \[
  \

Sea L ∈ R − {0}. Si (a_n)_{n∈N} satisface que lim_{n → +∞} \frac{a_n - L}{a_n + L} = 0, entonces lim_{n → +∞} a_n = ______.

Solve the limit problem involving a sequence (a_n) where L is a real number and the limit condition \frac{a_n - L}{a_n + L} = 0 holds as n approaches infinity. This problem explores the behavior of sequences and their limits in real analysis.

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