# Power series

1. May 22, 2005

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?

Last edited: May 22, 2005
2. May 22, 2005

I see it now no need to respond. thx

3. May 22, 2005

### Hurkyl

Staff Emeritus
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\leq for "less than or equal to".