Hi,
Could someone help me with these questions,I dont understand how you can find the radius of convergence:
1.f(x)=(1+4x)^3/2
State the radius of convergence of this power series
(I also had to use the General Binomial Theorem to determine the first four terms of the Taylor series at 0 for this series but I have done this)
2.g(x)=6(1+4x)^1/2
State the radius of convergence of this power series
(I also had to write down the first three terms of the Tayor series at 0 but I have done this)
No I have not learnt about that kind of series yet. ~It just seems it should be obvious because the question says "state" which implies it should be simple to detect the radius of convergence just by looking at the question. Thank-you for your replies Any more hinters as altough I'm trying my best I'm still not getting it . x
What do you know about power series?
No its not. If you expand a function as a power series about some point, the radius of convergence depends on which point you choose.~It just seems it should be obvious because the question says "state" which implies it should be simple to detect the radius of convergence just by looking at the question. Thank-you for your replies Any more hinters as altough I'm trying my best I'm still not getting it . x
Now if you specify that the expansion is about x=0 then you might get an answer.
RonL
ok for the first expansion I got: 1+6x+6x^2-4x^3
for 2.I got: -root6+1/root12x-1/root48x^2
Could you tell me where to go from here to state the radius of convergence? I'm struggling with the concept as I dont understand it. I only have a text book explanatin which is very brief!
Responses greatly appreciated
x