May someone check my work?

To find R

To find the interval of convergence, C

For :

which converges by alternating series test.

For :

which converges by the root test.

So C=

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- Apr 19th 2014, 10:19 AMMadSoulzRadius and interval of convergence
May someone check my work?

To find R

To find the interval of convergence, C

For :

which converges by alternating series test.

For :

which converges by the root test.

So C= - Apr 19th 2014, 04:46 PMjohngRe: Radius and interval of convergence
Hi,

No, you made an algebraic error. Given $a_n=n3^{-n}$, then $a_{n+1}=(n+1)3^{-n-1}$ and so the quotient

$${a_n\over a_{n+1}}={n3^{-n}\over (n+1)3^{-n-1}}=3\,{n\over n+1}$$

So your interval of convergence is $|x-2|<3$ or $-1<x<5$.

Aside. When you find the interval of convergence of a power series, the ratio test or root test will always fail at the endpoints; the interval of convergence is found by one of these tests. - Apr 19th 2014, 05:36 PMMadSoulzRe: Radius and interval of convergence
- Apr 20th 2014, 05:42 PMjohngRe: Radius and interval of convergence
Hi again,

Back to basics:

http://i61.tinypic.com/1zg965v.png