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If 1+x+x2n=a0+a1x+a2x2+.+a2nx2n , then

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By Expert Faculty of Sri Chaitanya
a
a0−a2+a4−a6+…=0 ,if n is odd
b
a1−a3+a5−a7+…=0,if n is even
c
a0−a2+a4−a6+….0, if n=4p,p∈I+
d
a1−a3+a5−a7+….=0, if n=4p+1,p∈I+
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detailed solution

Correct option is A

∵1+x+x2n=a0+a1x+a2x2+…+a2nx2nPutting x=i(i=−1)Then, we get1+i+i2n=a0−a2+a4−a6+…+ia1−a3+a5−a7+…⇒ in=a0−a2+a4−a6+…+ia1−a3+a5−a7+…if n is odd, then Re(in) = 0⇒ a0−a2+a4−a6+…=0if n is even, then Im (in) = 0⇒ a1−a3+a5−a7+…=0


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Similar Questions

 For n2, let Cr= rn  and an=r=0n 1Cr

Column-IColumn-II
A. r=0nrCrP. nan
B. r=0nnrCrQ. 1nan1
C. r=0n1 rCrR. 12nan
D.  r=0n11(nr)CrS. 12nan1

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