If $i^{2} = - 1$ , then sum $i + i^{2} + i^{3} + . . . . . . .$ to $1000$ terms is equal to

1

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i

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0

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Solution

The correct option is C $0$
Given,
$i^{2} = - 1$

$i + i^{2} + i^{3} + i^{4} . . . . . . . . . .$ upto 1000 term

$i^{3} = i^{2} . i = - i$
$i^{4} = (i^{2})^{2} = (- 1)^{2} = 1$

So sum is
$i - 1 - i + 1 + i - 1 - i + 1 + . . . . . . . . . . .$
$= 0$

Hence the sum is $0$ .

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Similar questions

If $i^{2} = - 1$ , then the sum $i + i^{2} + i^{3} + . . . . . .$ upto 1000 terms is equal to

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