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

[Drain Brain]

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]

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

 

[Drain Brain]

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?

 

[kaliprasad]

Hi kaliprasad! How did you choose the range?

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

 

[Drain Brain]

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.

 

[kaliprasad]

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