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I have to show the series is periodic, ##2\pi ## ( I think ), it is related to fourier - analyze fourrier course at academics, so I might be right, or just periodic, we learned only periodic of ## 2\pi ##

( of course also continuous, but that is easy, no need ).

My problem is, we have not learned how to show a series is perodic.

I know in order to show a function is perodic, I have to show ## f(x) = f(x+t) ##, but in series, I dont know how it will be... and also how can a series be periodic... it doesnt sound right to me...

I dont need a solution, just the beginning, what should I Do

should I do ## f(x)=f(x+T)## on the series? or something else?