Well the first one is just a geometric series with common ration . So you need .
Additionally, the root test states that the series converges absolutely if . So using what you have above, you will arrive at the same result.
I've calculated the radius of convergence for in two different ways and I get two different answers.Find the range of values of values of x for which the series and converge, and find an expression for their sums, carefully justifying your answers.
The first way:
Let .
Therefore
Hence .
Alternatively, using the ratio test:
This tells me that .
Which one is correct.
For :
The main problem I have now is trying to find the expression for the sums. Can someone show me how to do that?
That's one of my problems.Additionally, the root test states that the series converges absolutely if . So using what you have above, you will arrive at the same result.
Is it true that ?
Therefore the radius of convergence R should be .
However, when I use the ratio test (as seen in previous posts) I get . It seems odd that i'm getting two different answers
Sorry but I can't see the differenceNo, you are using , this is different from , that is where you problem is coming from.
On a lighter note, he's my working on the sums:
Finally, Shawsend i'm quite interested in solving what you've put. Unfortunately, what is the "a" in your ?