Find the sum `3^n C_0-8^n C_1+13^n C_2xx^n C_3+dot`

Explanation

To find the sum \( S = \sum_{r=0}^{n} (-1)^r \binom{3+r}{r} \), we can follow these steps:

### Step 1: Identify the General Term
The general term of the series can be expressed as:
\[ T_r = (-1)^r \binom{3+r}{r} \]
where \( r \) varies from \( 0 \) to \( n \).
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