Show that if f_{1} , f_{2} , ... , f_{n} are T-periodic functions, then a_{1}f_{1}+a_{2}f_{2}+ ... + a_{n}f_{n} is also T-Periodics. More generally, show that if sum (from n=1 to infinity) a_{n}f_{n}(x) converges to all x in (0,T], then its limit is a T-periodic function.
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