Find the value of Σn=1¹⁰⁰ iⁿ — JEE Mathematics
Find the value of $\sum_{n=1}^{100} i^n$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 13d ago
▲ 28
The sum is $i^1 + i^2 + i^3 + i^4 + \dots + i^{100}$.
We know that the sum of any four consecutive powers of $i$ is $0$ because $i + (-1) + (-i) + 1 = 0$.
The total number of terms is 100, which is perfectly divisible by 4 ($100 = 4 \times 25$).
Therefore, there are exactly 25 blocks of 4 terms, each summing up to 0.
$$Sum = 25 \times 0 = 0$$
Answer: 0
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Discussion (2)
VC
Can someone explain why we ignore the other root here?
DM
This is exactly the kind of step-by-step I needed. Respect.