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Question: Answered & Verified by Expert
If $i^2=-1$, then the value of $\sum_{n=1}^{200} i^n$ is
MathematicsComplex NumberJEE Main
Options:
  • A $50$
  • B $-50$
  • C $0$
  • D $100$
Solution:
1404 Upvotes Verified Answer
The correct answer is: $0$
$\sum_{n=1}^{200} i^n=i+i^2+i^3+\ldots .+i^{200}=\frac{i\left(1-i^{200}\right)}{1-i}$(since G.P.)
$=\frac{i(1-1)}{1-i}=0$

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