Determining Value of Power Series: How & Why?

[RadiationX]

How do you know what value a power series is centered at?

for example this power series is centered at 0:

$$\sum_{n=0}^\infty\frac{x^n}{n!}$$


what makes it centered at zero?



this one is centered at -1:

$$\sum_{n=0}^\infty{(-1)}^n{(x+1)}^n$$

the only thing i can discern is that when i perfrom the ratio test, for the secont series, i get this expression:

$$\lim_{n\rightarrow\infty}\vert{(-1)(x+1)}\\\vert$$ which is supposed to be less than 1.


what's the latex for the lessthan symbol?

 

[RadiationX]

I see it now no need to respond. thx

 

[Hurkyl]

what's the latex for the lessthan symbol?

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\leq for "less than or equal to".