[JEE Advanced 1998] the value of sum n 1 13 i n i n 1 where i
The value of $\sum_{n=1}^{13}(i^n+i^{n+1})$, where $i=\sqrt{-1}$, equals
(a) $i$
(b) $i-1$
(c) $-i$
(d) $0$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (b) $i-1$
$=(1+i)\sum_{n=1}^{13}i^n=(1+i)\cdot i=i-1$ (the period-4 sum leaves $i^{13}=i$).
JEE Advanced 1998 · Complex Numbers — verified solution by the Vidaara Team.
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