$i^{2} + i^{4} + i^{6} + . . . . . . . . . . (2 n + 1)$ terms equal to:

$i$

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$- i$

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$1$

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$- 1$

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Solution

The correct option is D
$- 1$

Evaluating the given series.
$\Rightarrow i^{2} + i^{4} + i^{6} + . . . . . . (2 n + 1) t e r m s = i^{2} + i^{4} + i^{6} + . . . uptosomeoddnumberofterms = - 1 + 1 - 1 + . . . uptooddnumberterms [T h e l a s t t e r m w i l l h a v e r e d u c e d p o w e r = 2] = - 1$
Hence, the correct answer is Option (D).

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i^{2} + i^{4} + i^{6} + . . .

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i^{2} + i^{4} + i^{6} + . . . + (2 n + 1)

i^{2} = - 1

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