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### Question 1: 
**Complete the following series:**

\[
\sum_{n=1}^{\infty} a_n
\]

The specific details of the series and method to complete it are unclear. Could you please clarify or describe the series in question?

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### Question 2:
**Determine if the following sequence converges or diverges:**

\[
\frac{2n^2 - 3n}{3n^2 + 5}
\]

I'll start solving this problem right away.

To determine if the sequence converges or diverges, we need to analyze the limit as \( n \to \infty \):

\[
\lim_{n \to \infty} \frac{2n^2 - 3n}{3n^2 + 5}
\]

Dividing the numerator and the denominator by \( n^2 \), we get:

\[
\lim_{n \to \infty} \frac{2 - \frac{3}{n}}{3 + \frac{5}{n^2}}
\]

As \( n \to \infty \), the terms \( \frac{3}{n} \) and \( \frac{5}{n^2} \) approach 0, so the expression simplifies to:

\[
\frac{2}{3}
\]

Thus, the sequence **converges** to \( \frac{2}{3} \).

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