Is the fnction in fourier series periodic?

Yes, a Fourier series represents a periodic function. It decomposes a periodic function into a sum of sine and cosine terms, each of which has a specific frequency. The resulting series will also be periodic, with the same period as the original function. If the original function is not periodic, it can still be approximated by a Fourier series over a finite interval, but the series itself will exhibit periodic behavior.