InterviewSolution
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InterviewSolution
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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` |
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Answer» 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` |
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