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2009 AMC 12A Question 15

AMC12 · 2009 AMC 12A

Question 15

For what value of $n$ is $$
\begin{aligned} &i + 2i^2 + 3i^3 + \cdots + ni^n \\ &= 48 + 49i? \end{aligned}
$$ Note: here $i = \sqrt{-1}.$
  1. $24$
  2. $48$
  3. $49$
  4. $97$
  5. $98$