If 
(x – 2) r = 
(x – 3) r and a k = 1 for all k ≥ n, then b n is equal to -
Text Solution
Verified by ExpertsB
Clearly, b n is the coefficient of (x – 3) n in the expression 
(x – 3) r . Therefore,
b n =Coefficient of (x–3) n in 
…(1)
= Coefficient of (x – 3) n in
= Coefficient of (x – 3) n in
( a k = 1 for all k ≥ n)
= Coefficient of (x – 3) n in 
= Coefficient of (x – 3) n in
= Coefficient of (x – 3) n in
= Coefficient of (x – 3) n+1 in {(x – 2) 2n+1 – (x – 2) n }
= Coefficient of (x – 3) n+1 in (x – 2) 2n+1
= Coefficient of (x – 3) n+1 in [(x – 3) + 1] 2n + 1
= Coefficient of (x – 3) n+1 in
= 2n+1 C n+1 .
Hence is correct answer.
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