Find the value of $1 + i^{2} + i^{4} + i^{6} + . . . + i^{2 n}$

1

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- 1

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it cannot be determined

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Solution

The correct option is D it cannot be determined
$S = 1 + i^{2} + i^{4} + i^{6} + . . . + i^{2 n} = 1 - 1 + 1 - 1 + . . . + (- 1)^{n}$
It depends on the value of $n$ . Hence, it cannot be determined unless $n$ is known.

Ans: D

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