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

Explanation

Since `(n+2)` th term is the middle term in the expansion of `(1+x)^(2n+n)`, we have `alpha = .^(2n+2)C_(n+1)`. Since `(n+1)` th and `(n+)` th terms are middle term in the expansion of `(1+x)^(2n+1)`. We have
`beta = .^(2n+1)C_(n)` and `gamma = .^(2n+1)C_(n+1)`
But `.^(2n+1)C_(n) + .^(2n+1)C_(n+1) = .^(2n+2)C_(n+1)` or `beta + gamma = alpha`