A "power series", a series of the form

has a "radius of convergence" but other kinds of series may not.

In particular, you can think of the series you are given,

as a

**geometric series**,

with

and

.

That's chisigma's point.

Now, you have probably learned, long ago, that the geometric series

will converge as long as |r|< 1. That's where chisigma gets

. In fact, since

is never negative,

which is equivalent to

or

. That's true for all x except ___ and the region of convergence is "all x except x= ___".