Hi I was reading my textbook, but I needed some clarity on the last step of the working out, how does the equation simplify from :
$x(t) = c_o + \sum_{n=1}^\infty c_n \exp(j n \omega t) + \sum_{n=1}^\infty c_{-n} \exp(-j n \omega t) $
TO
$x(t) = \sum_{n=1}^\infty c_1 \exp(j n \omega t)$
There are three parts, the first from -inf to -1, the second is 0, and the third from 1 to inf. then the total addition is from -inf to inf.
For the first part you could replace new(n) <- -old(n)
$$ x(t) = \sum_{n=-\infty}^{-1} c_n e^{nwt j}+c_0+\sum_{n=1}^{\infty} c_n e^{nwt j} $$ where: $$ \sum_{n=1}^{\infty} c_{-n} e^{-nwt j} = \sum_{n=-\infty}^{-1} c_n e^{nwt j}$$
It is possible to write the three terms in a single summation: $$ \sum_{n=-\infty}^{\infty} c_n e^{nwt j} $$