Radius/interval of convergence

[karadda]

Homework Statement

$$\Sigma$$ n!(2x-1)$$^{}n$$

from n=1 to infinity

Homework Equations

-ratio test

The Attempt at a Solution

lim n-> infinity | (n+1)!(2x-1)^(n+1) / n!(2x-1)^n |

lim n-> infinity | (n+1)(2x-1) |

|2x - 1| lim n-> infinity | (n+1) |

-1 < 2x -1 < 1

0 < 2x < 2
0 < x < 1
I know at this point I've done something pretty wrong. as my interval and radius doesn't match up with the back of the book. could use a push in the right direction, thanks.

 

[Dick]

What happened to the lim n->infinity |n+1|? Did you just drop it?

 

[karadda]

oh, I am not too sure what to do with it. i understand that the limit goes to infinity, UNLESS x = 1/2 in which case it goes to 0. how do i proceed knowing that?

nm, i should just stop there ;)

1/2 is the only value of x for which this will converge, so the interval of convergence is {1/2}. the radius is 0.

 

[Dick]

oh, I am not too sure what to do with it. i understand that the limit goes to infinity, UNLESS x = 1/2 in which case it goes to 0. how do i proceed knowing that?

nm, i should just stop there ;)

1/2 is the only value of x for which this will converge, so the interval of convergence is {1/2}. the radius is 0.

I couldn't have said it better myself.