find the radius of convergence and interval of convergence of the power series ∞∑ n=1 x^n/(n^2*3^n)

Question

find the radius of convergence and interval of convergence of the power series  ∞∑ n=1 x^n/(n^2*3^n)

turingtest · Answer

have you tried the ratio test?

anonymous · Answer

I dont even know where to start. i dont understand series and sequences.

anonymous · Answer

lim n->infinity of An+1/An

turingtest · Answer

that is a problem if you are doing power series and inervals of convergence and don't understand the basics...
but @nuk64 is pointing you the right way

anonymous · Answer

sorry, that's in absolute terms. so it's:
lim as n-> infinity of |An+1/An|

turingtest · Answer

@dillpickles do you know what nuk64 means by $$\lim_{n\to\infty}|{a_{n+1}\over a_n}|$$?

anonymous · Answer

Kind of. I understand that you plug in n+1 to the n's in the equation but my calc book is just confusing me. It has the equation with the n+1's multiplied by the inverse of the equation i think.. i dont understand why you need to multiply by the inverse.

turingtest · Answer

well I think you are looking at it like$$\lim_{n\to\infty}|a_{n+1}\cdot\frac1{a_n}|$$which is the same as I wrote above (it is still a ratio, hence the name ration test; it tests the limits between successive terms as $n\to\infty$

turingtest · Answer

so what is $a_{n+1}$ ?

anonymous · Answer

oh you are right haha hold on let me figure it out and i will show you

anonymous · Answer

try using this as an example. http://openstudy.com/users/nuk64#/updates/500e3969e4b0ed432e109689 i had trouble with this myself, but it's not too bad once you figure it out. :)

anonymous · Answer

oh and this one. http://openstudy.com/users/nuk64#/updates/500f4217e4b009397c67652c

anonymous · Answer

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