Interval of Convergence of Power Series with Square Root

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SUMMARY

The discussion centers on determining the interval of convergence for the power series $$\sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n$$. The user initially applied the root test, concluding an interval of convergence from 0 to 1. However, upon verification with Wolfram Alpha, the result indicated an interval from -1 to 1, which includes negative values. The confusion arises from the treatment of the absolute value within the square root, leading to the clarification that for real numbers, the domain must exclude negative values of x.

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

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