the coefficient of x^15 in the product of(1-x)(1-2x)(1-2^2x)...(1-2^15x) is.........?

plz give some hints also

Dear nishant

given question is a product of 16 brackets

and you can find  x¹⁵ only when x from 15 bracket is multiplied and constant term from 1 bracket.

so just multiply  

coefficient of x¹⁵ is  =-2 ^{1+2+3.....+15}   -2 ^{0+2+3+.....15}  ..................-2 ^{0+1+2+3...+14}

                                  =-2^{1+2+3.....+15} [1 +1/2 +1/2² +........1/2¹⁵]

                             =-2¹²⁰[2-1/2¹⁵]

                              =-2¹²¹ +2¹⁰⁵

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