I want to ask Question about the Fourier series in continuous time domain while reading a book signals and systems Alan Oppenheim. I have confusion in understanding the statement on page 189 of its 2nd edition.
To derive alternative form of Fourier series, we first rearrange the summation in Eq.3.25 as
$$x(t) = \sum^{+\infty}_{k\ =\ 1} [a_k e^{jk\omega_0t}+a_{-k} e^{-jk\omega_0t}]$$
where Eq. 3.25$$x(t) = \sum^{+\infty}_{k\ =\ -\infty} a_k e^{jk\omega_0t}$$
I want to know two things
1) How summation from -infinity to +infinity changes to 1 to +infinity
2) How we get this term $$a_{-k} e^{-jk\omega_0t}$$ in the equation.