The discussion revolves around determining the number of terms in the summation $\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$. Participants explore the reasoning behind the conclusion that there are $2N + 1$ terms in this summation, focusing on the range of values for \( n \) from \(-N\) to \(N\).
Participants generally agree on the conclusion that there are \(2N + 1\) terms, but there is some confusion regarding the counting method and the choice of range, indicating a lack of consensus on the reasoning process.
Some participants express uncertainty about the counting method and the implications of different ranges, which may affect their understanding of the total number of terms.
Drain Brain said:I just want to know how do I determine the number of terms will be in this summation. The answer to this 2N+1 terms. I can only arrive at preliminary steps of solving this. can you tell why 2N+1 is the number of terms? I know that the magnitude of complex exponential function squared would result to one.
$\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$
kaliprasad said:as n is from -N to N the total number of terms is N ( -N to -1) + 1 ( zero) + N ( 1 to N) = 2N + 1
Within parenthesis I have mentioned the range
Drain Brain said:Hi kaliprasad! How did you choose the range?
kaliprasad said:In the sum that is (sigma) n is from -N to N and hence the range
Drain Brain said:why it is only -N to -1, 0, and 1 to N? I'm thinking of other ranges like -N to -2 etc.. I'm confused. Please help.