How can I prove peroidic of state of simple harmonic

[Asal]

Hi
How can I prove peroidic of state of simple harmonic

Y(x)=exp(iwt/2 sum(Cn Un (x) exp(-iwnt) )

 

[berkeman]

Hi
How can I prove peroidic of state of simple harmonic

Y(x)=exp(iwt/2 sum(Cn Un (x) exp(-iwnt) )

Welcome to the PF. How would you usually approach proving that a function was periodic?

 

[Asal]

I usually use f(x+t)=f(x), but here I am not sure how can I prove it.