Period of the function f(x) =sinx+tanx2+sinx22+tanx23+...+sinx2n−1+tanx2n  is

f(x) =sinx+tanx2+sinx22+tanx23+...+sinx2n−1+tanx2n Each of the function on the right is periodic with periods 2π,2π,22π,22π,...,2nπ,2nπ Hence, f(x)  is periodic with period 2nπ .