Periodicity of a Function: How to Determine if a Function is Periodic

[rafnhy]

Hello, I have got a question about the periodicity of a function.
I know that in discrete domain, a periodic function have to verify
x[n] = x[n+N]
where N is the positive integer and foundamental period.
My problem is that if I have a function like this: e^(j3π(n+1/2)/5),
how can I confirm if that the function can be periodical?
I attemted to use the Euler equivalent, but still no solution came to my mind.
Thank you!

 

[omkar13]

I attached a photo.It's not so clear but I hope you can understand the content in it.According to that discussion,I found that given func. is not periodic.