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

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rafnhy
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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!
 
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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.
 

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