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

Question

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

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`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

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`