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.
Determining terms in a summation allows us to analyze the behavior of a sequence or series, and understand the overall pattern and behavior of the terms.
To determine the terms in a summation, we first need to identify the general form of the terms, and then substitute different values for the index variable to find the corresponding values of the terms.
This notation represents a summation of the squared absolute values of the terms in the sequence $e^{J\frac{\pi}{4}n}$, where $n$ ranges from $-N$ to $N$.
Determining terms in a summation can be useful in areas such as calculus, where it can help in finding the limit of a sequence or series, and in statistics, where it can be used to analyze the behavior of data over time.
Yes, in some cases, the terms in a summation can be determined using a formula or a pattern. However, in more complex cases, it may require a more thorough analysis and substitution of values to determine the terms.