Find the sum `1 xx 2 xx .^(n)C_(1) + 2 xx 3 xx .^(n)C_(2) + "….." + n xx (n+1) xx .^(n)C_(n)`.

Explanation

To find the sum \( S = 1 \cdot 2 \cdot \binom{n}{1} + 2 \cdot 3 \cdot \binom{n}{2} + \ldots + n \cdot (n+1) \cdot \binom{n}{n} \), we can express this sum in a more manageable form.

### Step-by-Step Solution:

1. **Express the Sum**:
The given sum can be expressed in summation notation:
\[
S = \sum_{r=1}^{n} r(r+1) \binom{n}{r}
...