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the coefficient of x 49 in the expansion (x-1)()(x-1/2)(x-1/2 2 )........(x-1/2 49 ) is???

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

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 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

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