Show that `S_(n)=(n(2n^(2)+9n+13))/(24)`.

Explanation

To show that \( S_n = \frac{n(2n^2 + 9n + 13)}{24} \), we will start by finding the nth term \( T_n \) and then derive \( S_n \) from it.

### Step 1: Define the nth term \( T_n \)
The nth term \( T_n \) can be expressed as:
\[ T_n = S_n - S_{n-1} \]
Given \( S_n = \frac{n(2n^2 + 9n + 13)}{24} \), we need to find \( S_{n-1} \).
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