91Ó°ÊÓ

Find the Fourier series of $$ f(x)= \begin{cases}x-[x], & x \text { is not an integer, } \\ \frac{1}{2}, & x \text { is an integer. }\end{cases} $$ To what values does the Fourier series converge at the points \(x=5, x=3\), and \(x=1.5\) ?

Find the complex Fourier series of \(f(t)=\frac{1}{1-\frac{1}{2} e^{-i t}}\) on the interval \([-\pi, \pi]\).