If the coefficient of the middle term in the expansion of `(1+x)^(2n+2)i salpha` and the coefficients of middle terms in the expansion of `(1+x)^(2n+1)` are `beta` and `gamma` then relate `alpha,betaa n dgammadot`

Explanation

To solve the problem, we need to find the coefficients of the middle terms in the expansions of \( (1+x)^{2n+2} \) and \( (1+x)^{2n+1} \), and then relate these coefficients, denoted as \( \alpha \), \( \beta \), and \( \gamma \).

### Step-by-Step Solution:

1. **Identify the Middle Term in \( (1+x)^{2n+2} \)**:
- The total number of terms in the expansion of \( (1+x)^{2n+2} \) is \( 2n+3 \) (since the number of terms is \( k+1 \) for \( (1+x)^k \)).
- The middle term is the \( (n+1)^{th} \) term.
- The coefficient of the middle term is given by:
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