How to represent this discrete function?

[iScience]

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?

 

[LCKurtz]

See this thread:
https://www.physicsforums.com/threads/how-do-i-represent-this-sine-function.803221/

 

[SammyS]

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?

I suspect that "N=2k-1 where k=1, 2, ... " is simply a portion of the solution given by your book.

Which values of N are given by these values of k ?

By The Way: You need to state the problem to be solved, in the body of you post - - a complete statement - - regardless of the title of the Thread.