MHB Determining Terms in $\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$

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The summation $\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$ contains a total of 2N + 1 terms. This is determined by counting the range of n from -N to N, which includes N negative values, zero, and N positive values. The magnitude of the complex exponential function squared equals one, confirming that each term contributes equally. The confusion arose from considering alternative ranges, but the correct count is based on the specified limits. Thus, the total number of terms in the summation is indeed 2N + 1.
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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.

$\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$
 
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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.

$\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$

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
 
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

Hi kaliprasad! How did you choose the range?
 
Drain Brain said:
Hi kaliprasad! How did you choose the range?

In the sum that is (sigma) n is from -N to N and hence the range
 
kaliprasad said:
In the sum that is (sigma) n is from -N to N and hence the range

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.
 
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.

Sorry for the confusion. I counted the number of -ve values, positive values and zero separately. from -N to +N it is 2N+1 values
 
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