<p>Ok so here are some questions from a "mock" AP exam test that I don't get how to do</p>
<p>2) The **sequence<a href="r">/b</a>^n converges if and only if<br>
A: | r | < 1<br>
B: | r | ≤ 1<br>
C: − 1 < r ≤ 1<br>
D: 0 < r < 1<br>
E: | r | > 1<br>
I know that if that was a series I use the geometric test.... but it's a sequence...</p>
<p>14) The series n!(x-3)^n converges if and only if
F: x = 0<br>
G: 2 < x < 4<br>
H: x = 3<br>
J: 2 ≤ x ≤ 4<br>
K: x < 2 or x > 4 x > 4<br>
When I do the ratio test, I end up with |x-3|lim = infinity... i know that if the limit is infinity, the interval of convergence is 0, but would the "|x-3|" in front do anything?? would it change the IOC to x=3?? </p>
<p>17) Tha radius of convergence for the series [(x^n)(n^n)/(2^n)(n!)] is
A: 0
B: 2/e<br>
C: e/2<br>
D: ∞<br>
E: none of these
When I do the ratio test, I end up with |x/2|lim=e, so the radius of convergence would be e/2 (L/2) but I have |x/2| up front... so would that change my ROC?? </p>
<p>i’ll give it a try
2. Hmm… r is always less than 1, because as n approaches infinity, the limit is 0. so r must be less than 1. That knocks out a few answers~~
Hm. I dont think negative values of r would world, because we want it to approch 0. negative values of r would kinda ruin it,because it’ll fluctuate above/below the x axis,depending on the nth degree.
So my guess would be …</p>
<p>D)</p>
<p>14) I’m kinda iffy on these too. but i think u’re right. i arrived on the same thing… um. limit goes to infinity… like u said, x=3 would make the whole thing 0, which will converge at this interval(x=3)
so C)
heres some notes i found useful:
[Pauls</a> Online Notes : Calculus II - Power Series](<a href=“http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeries.aspx]Pauls”>Calculus II - Power Series)</p>
<p>17)
hm
i dont know how to do the last one because i’m not really good at root tests…im pretty sure root test works wel on this one because of the n powers~</p>
<p>17) The final answer I got was: |x/2|lim = e</p>
<p>I learned that to find the radius of convergence, you divide the limit by 2… so in this case the radius of convergence would be e/2…right? but would that |x/2| in front change anything…?</p>
<p>and also, for the first one, are sequences really the same thing as series?</p>
