**Problem:** Find the Fourier series and its sum for the following
function:

**Solution:**
This seems to be a standard problem, so we use the
usual procedure.
When we extend the given function periodically, its period will be
*T* = 2.*ω* = π.

Since *f* is even, the fact that
*b*_{k} = 0

To find the sum of this series we use
Jordan's conditions. First
we draw the periodic extension of the given function *f*. Then we
should check on points of discontinuity, but there are none. Thus the
Fourier series converges to this periodic extension, and the convergence is
uniform on the whole real line.

**Remark:** What do we get if we substitute
*t* = 1?

What do we get if we substitute
*t* = 0?