(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to find for which values of x the following converge

2. Relevant equations

[tex]\sum n x^{n}[/tex]

[tex]\sum \frac{x^{n}}{n}[/tex]

[tex]\sum n^{n} x^{x}[/tex]

3. The attempt at a solution

I used the ratio test for the first two and the root test for the last and found respectively that x must lie within

(-1,1)

[-1,1)

{0}

Are these right?

and

Is this the right way to go all the time?

I was wondering when I'll be able to apply the ratio/root tests for radii of convergence. Is it just when we have power functions?

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# Homework Help: I was wondering why this works and if it works every time

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