If the expansion in powers of x of the function ( 1 − a x ) ( 1 − b x ) 1 is a 0 + a 1 x + a 2 x 2 + a 3 x 3 + … , then a n is

Question

If the expansion in powers of x of the function ( 1 − a x ) ( 1 − b x ) 1 ​ is a 0 ​ + a 1 ​ x + a 2 ​ x 2 + a 3 ​ x 3 + … , then a n ​ is

TestHub · Accepted Answer

( 1 − a x ) − 1 ( 1 − b x ) − 1 = ( 1 + a x + a 2 x 2 + …… ) ( 1 + b x + b 2 x 2 + … . ) ∴ coefficient of x n = b n + a b n − 1 + a 2 b n − 2 + … . + a n − 1 b + a n = b − a b n + 1 − a n + 1 ​ ∴ a n ​ = b − a b n + 1 − a n + 1 ​

Mathematics - Binomial Theorem Question with Solution | TestHub

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