Coefficient of α t in the expansion of α + p m - 1 + α + p m - 2 α + q + α + p m - 3 α + q 2 + . … … … + α + q m - 1 , where α ≠ - q and p ≠ q is

Question

Coefficient of α t in the expansion of α + p m - 1 + α + p m - 2 α + q + α + p m - 3 α + q 2 + . … … … + α + q m - 1 , where α ≠ - q and p ≠ q is, C m t p t - q t p - q, C m t p m - t - q m - t p - q, C m t p t + q t p - q, C m t p m - t + q m - t p - q

MARKS App · Accepted Answer

The terms are in GP with a = α + p m - 1 , r = α + q α + p and number of terms = m . S = α + p m − 1 α + q α + p m − 1 α + q α + p − 1 = α + q m - α + p m q − p Coefficient of α t in 1 q - p α + q m - α + p m = 1 q - p C t m q m - t - C t m p m - t = C t p m - t - q m - t m p - q

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