Multiple choice

The sum of the series $i+2i^{2}+3i^{3}+...$ up to $200$ terms equals

  1. $100\left ( i-1 \right )$
  2. $100\left (1- i \right )$
  3. $200i$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The series is S = i + 2i^2 + 3i^3 + ... + 200i^200. This is an arithmetico-geometric series. Using the formula for such series or by grouping terms (i - 2 - 3i + 4 + 5i - 6 - 7i + 8...), the sum evaluates to 100(1 - i).

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