• Mar 15th 2010, 02:28 PM
The problem says to find the radii of convergence of these two functions:

$\displaystyle 2-\sqrt{1+x^2}$

$\displaystyle 1-\ln{(1+x^2)}$

But I am not sure how to do this. Could you just take the limit of each and set that to be less than 1? I am just not sure how to approach this problem. Thanks ahead of time for the help.
• Mar 15th 2010, 02:53 PM
Miss
Quote:

The problem says to find the radii of convergence of these two functions:

$\displaystyle 2-\sqrt{1+x^2}$

$\displaystyle 1-\ln{(1+x^2)}$

But I am not sure how to do this. Could you just take the limit of each and set that to be less than 1? I am just not sure how to approach this problem. Thanks ahead of time for the help.

"Raduis of convergence" for the infinite series only ..
I do not see any series here ..
• Mar 15th 2010, 06:54 PM
Quote:

Originally Posted by Miss
"Raduis of convergence" for the infinite series only ..
I do not see any series here ..

That's partly why I am stuck and if that is the case, then I will make sure to bring it up with my instructor.
• Mar 15th 2010, 08:02 PM
Quote:

The problem says to find the radii of convergence of these two functions:

$\displaystyle 2-\sqrt{1+x^2}$

$\displaystyle 1-\ln{(1+x^2)}$

But I am not sure how to do this. Could you just take the limit of each and set that to be less than 1? I am just not sure how to approach this problem. Thanks ahead of time for the help.

You may write these as infinite series...

$\displaystyle 2-\sqrt{1+x^2}=2-\left(1+x^2\right)^{\frac{1}{2}}$

This may be expanded as a series, as can the natural log.