I run the ratio test, get a radius, and then lose points on the interval part.
Accepted answer
The **radius** `R` comes straight out of the ratio test: solve `|x − c| < R`. That gives you an open interval `(c − R, c + R)` where the series definitely converges.
The **interval** of convergence is that set plus a verdict on the two **endpoints** — and the ratio test cannot decide them. At `x = c ± R` the limit equals exactly 1, which is the inconclusive case.
So you must substitute each endpoint back into the original series and test the resulting numeric series on its own (often alternating series test at one end, p-series or nth-term at the other). Each endpoint is decided separately; it's common for one to converge and the other to diverge. Writing the interval with the wrong bracket is the usual lost point.