<p>hey guys,
I would really appreciate it if you could help me with this question:
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)</p>
<p>(summation from 1 to infinity) of (-1)^(n+1) times (4n-1)(x-3)^n, all that divided by 4^n</p>
<p>thank you</p>
<p>Okay, well first a few hints: Use the ratio test on the non-alternating part to find the interval of convergence, test if those converge, then test if they converge by re-introducing the alternating component and using the alternating series test.</p>
<p>The interval is 2<x<4 so all you need to do now is test these end points with two conditions: one with the series alternating, and the other without.</p>
<p>Okay well I worked through it. I'm also in Calc BC AP but I don't remember much from this section. I got that the series converges absolutely along the entire interval, even at the end points.</p>
<p>cbf88, how'd you get that interval? my interval after the ratio test was (-1,7)...please help because i'm studying bc independently!!</p>