Find the sum of `n` terms of the series `1. 2^2+2. 3^2+3. 4^2+......`

Explanation

To find the sum of the first \( n \) terms of the series \( S_n = 1 \cdot 2^2 + 2 \cdot 3^2 + 3 \cdot 4^2 + \ldots \), we can follow these steps:

### Step 1: Identify the General Term
The general term of the series can be expressed as:
\[ T_r = r \cdot (r + 1)^2 \]
where \( r \) is the term number starting from 1.
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