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Question

The coefficient of x5 in (1+2x+3x2+.....)−3/2 is

A
21
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B
25
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C
26
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D
None of these
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Solution

The correct options are
A None of these
D 26
Solution:- (D) None of these
Let S=1+2x+3x2+.....
xS=x+2x2+3x3+.......
SxS=1+x+x2+x3+.......
As the above sequence is a G.P. of infinite terms.
S(1x)=11x[Sum of infinite terms of g.p. of common ration r=11r]
S=1(1x)2=(1x)2
(1+2x+3x2+.....)32=((1x)2)32=(1x)3
As (1x)3=1x33x+3x2
Since there is no term of x5 in the above expansion.
Hence the coefficient of the x5 in the above expression is 0.

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