Find the sum to n terms of the series :`1 xx 2 + 2 xx 3 + 3xx4 + 4xx5+. . . . . .`

Explanation

To find the sum to n terms of the series \( S = 1 \times 2 + 2 \times 3 + 3 \times 4 + 4 \times 5 + \ldots \), we can follow these steps:

### Step 1: Identify the General Term
The \( r \)-th term of the series can be expressed as:
\[ T_r = r \times (r + 1) = r^2 + r \]

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