- #1
RadiationX
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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?
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:
