1hey sky is the answer b)........---->.......[12][12][12]........
the coeff of x14 in the product
(1-x)(1-2x)(1-22x)......(1-215x) is equal to,
given that
1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}}.... + \frac{1}{2^{15}}= a
and
1 + \frac{1}{2^{2}} + \frac{1}{2^{4}}.... + \frac{1}{2^{30}}= b
is :-
a) 2^{119}(a^2 - b)
b) 2^{120}(a^2 - b)
c) 2^{120}(b-a^2)
d) 2^{119}(b-a^2)
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8 Answers
1how did it seem wrong ?
waise i too did b..
and very sorry .. i have no answers.......
1it\ can\ be\ written\ as\ \\ \\ 2^{120}(x-1)(x-\frac{1}{2})(x-\frac{1}{2^2})...(x-\frac{1}{2^{15}})\\ \\ so\ coff.\ of \ x^{14}\ is\ sum\ of\ roots\ taken\ two\ at\ a\ time\\ \\ so\ 2S_2=-2^{120}(a^2-b)\\ \\ => S_2 = 2^{119}(b-a^2)
so ans must be (D)