My high school teacher gave us the following problem:
The coefficients of the power series (starting at n=0 and continuing for all real numbers) an(x-2)n satisfy a0 = 5 and an = ((2n+1)/(3n+1))an-1 for all n≥1. What is the radius of convergence of the series?
I've been taught to use the "ratio" test. Effectively placing the n+1 term over the nth term, simplifying, and then evaluating. Based on my work I believe that the answer should be 0, but am unsure whether it is correct due to that fact that I was absent when the material was taught.
P.S. Does anyone know how to write sigma notation in a word processor or in html?