Interval of Convergence of Power Series with Square Root

  • #1
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.
 

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  • #2
LCKurtz
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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.
 
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  • #3
Thank you for the help in clearing up my confusion.
 

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