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Find the value of 1+i^(2)+i^(4)+i^(6)+....

Find the value of `1+i^(2)+i^(4)+i^(6)+...+i^(2n),`

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`i^{1}=i `

`i^{2}=-1 `

`i^{3}=-1 `

`i^{4}=1`

Other powers of i can be easily found out.

`i^{5}=i^{2} i^{3}=-1 -i=i`

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