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If , then
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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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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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