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The sequence $S = i + 2 i^{2} + 3 i^{3} + 4 i^{4} + \dots$ up to 100 terms simplifies to, where $i = \sqrt{- 1}$

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50(1−i)

25i

25(1+i)

100(1−i)

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Correct option is A

S=i+2i2+3i3+⋯+100i100S⋅i=i2+2i3+⋯+99i100+100i101S(1−i)=i+i2+i3+⋯+i100−100i101S(1−i)=i+i2+i3+i4+i5+i6+i7+i8⇒ S(1−i)=0+0+⋯+i97+i98+i99+i100−100i⇒ S=−100i1−i=−100i(1+i)(1−i)(1+i)⇒ S=−50(i−1)∴ S=50(1−i)

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The sequence S=i+2i2+3i3+4i4+⋯ up to 100 terms simplifies to, where i=−1

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The sequence $S = i + 2 i^{2} + 3 i^{3} + 4 i^{4} + \dots$ up to 100 terms simplifies to, where $i = \sqrt{- 1}$