Co-efficient 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 :

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E = ( α + p ) m − 1 + ( α + p ) m − 2 ( α + q ) + ⋯ + ( α + q ) m − 1 This is a geometric series with ratio α + p α + q ​ : E = ( α + p ) − ( α + q ) ( α + p ) m − ( α + q ) m ​ = p − q ( α + p ) m − ( α + q ) m ​ ⇒ co-efficient of α t = p − q m C t ​ ( p m − t − q m − t ) ​

Mathematics - Binomial Theorem Question with Solution | TestHub

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