" (i) "i^(2)+i^(4)+i^(6)+...+(2n+1)" terms "

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Simplifiy i^(2)+i^(4)+i^(6)+.....+(2n+1) terms

i^(2)+i^(4)+i^(6)+ldots . .(2 n+1) terms =

If (i)^(2) = -1, (i)^(2) + (i)^(4) + (i)^(6) + ...... to (2n + 1) terms =

1 + i^(2n) + i^(4n) + i^(6n)

1+i^(2)+i^(4)+i^(6)+... .+i^(2 n)=

1 + i^(2) + i^(4) + i^(6) = 0 .

The value of i^(2)+i^(4)+i^(6)+i^(8)... upto (2n+1) terms,where i^(2)=-1, is equal to: