Find the sum of the series: `1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.`

Explanation

To find the sum of the series \( S = 1 \cdot n + 2 \cdot (n - 1) + 3 \cdot (n - 2) + \ldots + (n - 1) \cdot 2 + n \cdot 1 \), we can follow these steps:

### Step 1: Identify the General Term
The series can be expressed in terms of a general term \( T_r \):
\[ T_r = r \cdot (n - r + 1) \]
where \( r \) ranges from 1 to \( n \).
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