Please help with polar coordinates explanation. Thanks.
the 2n + 1 generates odd numbers. it simply means you add or subtract odd multiples of pi.
so say you have $\displaystyle (r, \theta ) = (1, \pi)$
then that is the same as saying $\displaystyle (-1, 2 \pi) = (-1, 3 \pi) = (-1, 4 \pi) = ... = (-1, - \pi) = (-1, -2 \pi) = ...$ and so on.
to really get what's going on, try plotting all these points on a diagram, you'll see the pattern