Find the sum of the series `1xxn+2(n-1)+3xx(n-2)++(n-1)xx2+nxx1.`

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 \( r \)-th term of the series can be expressed as:
\[ T_r = r \cdot (n - r + 1) \]
for \( r = 1, 2, 3, \ldots, n \).
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