The coefficient of x^ 2^ n+1 in 1 (1 + x)(1 + x^2)(1 + x^4) (1 + x^ 2^n ) , where |x| < 1, is

JEE Advanced Mathematics question

The coefficient of in , where , is

Answer: (B)

Multiply numerator and denominator by and collapse the product using repeatedly:

(1-x)(1+x)(1+·s(1+ = 1 - .

Hence, with and ,

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Question ID VK-110373