Considering the function $\displaystyle u(t,x)=\sum_{h=1}^{\infty}\left(a_{n}\cos\frac{n\p i}{L}ct+b_{n}\sin\frac{n\pi}{L}ct\right)\sin\frac{ n\pi}{L}x$

I know that the period of this function is $\displaystyle 2\pi/L$, but I am not sure how to prove it. I tried plugging in the period for t and reducing, but didn't get very far. Is this the right approach? Can anyone help with this?

Thanks in advance!