So I had to calculate the radius of convergence of
around the point
This is how I tried it. I'd love to hear what is wrong with my attempt:http://www.sb.hik.se/personal/sanno/.../Chapter_5.pdf
V.4.1.f) The Answer is 2.
First I rewrote it
Then with partial fractioning:
So we can write are original function as :
And use the geometric series formula:
And finally apply the ratio test to the coefficients:
So I guess R would be one.
Please, not only advise me how to find the radius of convergence. Please tell me if I made any mistakes above (particularly in method.)
Thanks. Although I made I mistake so the function your looking at isn't correct.
But I could say has poles in and then reason like you did...
I did a partional fractioning and got:
And then rewrote it to a form with an easy geometric series approach.
So for example
Gives
And that's just for the first part.... that's a lot of work....
Another one, -note this is not my homework I am trying to grasp it and got the solutions- which I found hard.
What is the radius of convergence of around
Well I tried and I tried, but couldn't rewrite it nicely.
Solution:
Rewrite
The singularities are and the distance from 2 to the nearest is
Well this seems very farfetched to me. How could I have come up with this rewriting myself?