# Interval of Convergence of Power Series with Square Root

I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well.
$$\sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$
Find the interval of convergence?
I tried using the root test and got from 0 to 1 but when I checked with Wolfram and it gave from -1 to 1 saying the absolute value would go inside the square root. Am I doing something wrong or is Wolfram making a mistake. Thanks in advance for any help.

LCKurtz
Homework Helper
Gold Member
I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well.
$$\sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$
Find the interval of convergence?
I tried using the root test and got from 0 to 1 but when I checked with Wolfram and it gave from -1 to 1 saying the absolute value would go inside the square root. Am I doing something wrong or is Wolfram making a mistake. Thanks in advance for any help.
Assuming ##x## is real, ##x<0## is not in the domain.

• Satirical T-rex
Thank you for the help in clearing up my confusion.