The discussion focuses on representing the discrete function defined by the equation sin(Nπ/2) for N = 1, 2, 3, ... The values of the function are f(1) = 1, f(2) = 0, and f(3) = -1. A proposed solution, -1/2(-1)^N, is identified as incorrect. The book suggests using the substitution N = 2k - 1, where k = 1, 2, ..., to derive the correct values, prompting further clarification on how this substitution works.
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I suspect that "N=2k-1 where k=1, 2, ... " is simply a portion of the solution given by your book.iScience said:Homework Statement
my function: sin\frac{N\pi}{2} , N = 1, 2, 3, ...
N = 1 ---> f(N) = 1
N = 2 ---> f(N) = 0
N = 3 ---> f(N) = -1
Homework Equations
The Attempt at a Solution
-\frac{1}{2}(-1)^N
obviously it's wrong but just an 'attempt'
my book refers to the substitution N=2k-1 where k=1, 2, ...
but i don't understand how this returns the correct values.
any thoughts?