The question you uploaded is asking to check which of the following series statements are true regarding different types of convergence on certain intervals.

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Question 8:
Among the following statements, check the ones that are true:

a. The series $\sum_{n \in \mathbb{N}} \frac{e^{-nt}}{n}$ converges simply on $]0, +\infty[$.

b. The series $\sum_{n \in \mathbb{N}} \frac{e^{-nt}}{n^2}$ converges normally on $]0, +\infty[$.

c. The series $\sum_{n \in \mathbb{N}} \frac{e^{-nt}}{n^2}$ converges uniformly on $]1, +\infty[$.

To solve this, we must analyze each series for different types of convergence:

1. Simple convergence means that for each fixed $t$, the series converges as $n \to \infty$.
2. Normal convergence usually refers to convergence in a stronger sense (e.g., absolute convergence or convergence of integrals), which is often required for stronger functional properties.
3. Uniform convergence means that the series converges uniformly over the entire interval, not just pointwise.

Let me know if you'd like a detailed analysis of each of these options!