COMEDK · Maths · 3. Complex Number
The maximum value of \(n < 101\), such that \(1+\sum_{k-1}^{n} i^{k}=0\) is
- A 96
- B 97
- C 99
- D 100
Answer & Solution
Correct Answer
(C) 99
Step-by-step Solution
Detailed explanation
We have, \(\sum_{n=1}^{n} i^{k}=i+i^{2}+i^{3}+i^{4}+i^{5}+i^{6}+i^{7}+i^{8}+i^{9}+\ldots\) Now as, \(i^{4}=i^{8}=i^{12}=\ldots i^{n}=1\) and \(i+i^{2}+i^{3}+i^{4}=0\) So, \(\sum_{n=1}^{n} i^{k}=i+i^{2}+i^{3}+i^{4}+i+i^{6}+\ldots i^{7}+i^{8}+i^{2}+\ldots\)…
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