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

∵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