The sequence $S = i + 2 i^{2} + 3 i^{3} + . . . . . . .$ upto 100 times simplifies to where $i = \sqrt{- 1}$ .

50 (1 - i)

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25 i

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25 (1 + i)

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100 (1 - i)

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Solution

The correct option is A $50 (1 - i)$
$S = i + 2 i^{2} + 3 i^{3} \dots + 100 i^{100} S = i - 2 - 3 i + 4 + \dots + 100 S = i (1 - 3 + 5 \dots) + (- 2 + 4 \dots) S = 50 - 50 i = 50 (1 - i)$

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100

i + 2 i^{2} + 3 i^{3} + \dots

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i = \sqrt{- 1}

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100

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