Summation of Series: Is the Radius from -∞ to ∞?

[MozAngeles]

Homework Statement

sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity?
after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x).
is this right?
if not can you steer me in the right direction, please.

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity?
after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x).
is this right?
if not can you steer me in the right direction, please.

Looks good to me.

 

[MozAngeles]

thanks