the coefficient of x49 in the expansion (x-1)()(x-1/2)(x-1/22)........(x-1/249) is???

Hello student,Please find the answer to your question belowGiven expression is=(x-1)(x-1/2)(x-1/22)........(x-1/249)=x50-((1/2)0+(1/2)1+.......+(1/2)49)x49+.......so coefficient of x49=(1/2)0+(1/2)1+.......+(1/2)49As there are in GP with a common ratio r=(1/2) with a=1coefficient of x49=1(((1/2)50-1)/(1/2)-1) =(250-1)/250

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Grade 12Algebra

the coefficient of x⁴⁹ in the expansion (x-1)()(x-1/2)(x-1/2²)........(x-1/2⁴⁹) is???

Mostafijur Rahaman

11 Years agoGrade 12

1 Answer

SHAIK AASIF AHAMED

Approved Tutor Answer11 Years ago

Hello student,
Please find the answer to your question below
Given expression is
=(x-1)(x-1/2)(x-1/2²)........(x-1/2⁴⁹)
=x⁵⁰-((1/2)⁰+(1/2)¹+.......+(1/2)⁴⁹)x⁴⁹+.......
so coefficient of x⁴⁹=(1/2)⁰+(1/2)¹+.......+(1/2)⁴⁹
As there are in GP with a common ratio r=(1/2) with a=1
coefficient of x⁴⁹=1(((1/2)⁵⁰-1)/(1/2)-1)
=(2⁵⁰-1)/2⁵⁰