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clooneyisagenius

Member

Registered: 2007-03-25

Posts: 56

Find radius of convergence for:

Find radius of convergence for:

What I know / have done:

I know I am supposed to use the limit ratio test.

So I got

.
But I'm having trouble finding the limit of that.

[side note: then I take the limit of that, say L, and do L|x|<1??? and the radius of convergence is 1/L?]

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Find radius of convergence for:

It looks like using the root test would be far easier.

Clearly,

The limit as k --> ∞ is therefore 1/2 and so the radius of convergence is 2.

---

Why did the vector cross the road?
It wanted to be normal.

clooneyisagenius

Member

Registered: 2007-03-25

Posts: 56

Re: Find radius of convergence for:

You're right.  I was looking in the textbook. And it said use the ratio test but looking at the reason WHY i see that root test is the same. And as you point out above is CLEARLY easier.

So my 2nd question is this:
If I graph the summands for n=3,6,9, and 12. I get:
http://render-2.snapfish.com/render2/is=Yup6aQQ%7C%3Dup6RKKt%3Axxr%3D0-qpDPfRt7Pf7mrPf
rj7t%3DzrRfDUX%3AeQaQxg%3Dr%3F87KR6xqpxQQ0QxJPPxQ0oxv8uOc5xQQQGloQnaanGPqpfVtB
%3F*KUp7BHSHqqy7XH6gX0QPGe%7CRup6GQP%7C/of=50,590,369
(dont think i can add pics to this)

Then the question asks, "do you expect convergence at either or both of the endpoints of the interval of convergence of the infinite series and prove it."

I'm not sure what this is asking?
Is it asking if the summands approach 0 when |x| equals the radius of convergence? or...?

Last edited by clooneyisagenius (2008-03-20 12:15:14)