anonymous
  • anonymous
how do we know if this is a power series 1+x+(x-1)^2+(x-2)^3+(x-3)^4+...
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Since this is not centered around a point (you are subtracting different values from x each time), it is not a power series.
myininaya
  • myininaya
because everything is in the form of (x-n)^(n+1) starting with n=-1. doesn't that make it a power series?
myininaya
  • myininaya
http://en.wikipedia.org/wiki/Power_series says it is

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anonymous
  • anonymous
No, a power a series is a series of the form \[\sum_{n=0}^{\infty}c _{n}x ^{n} = c_{0}+c_{1}x+c_{2}x^{2}+....+c_{n}x^{n}+...\] or \[\sum_{n=0}^{\infty}c_{n}(x-a)^{n}=c_{0}+c_{1}(x-a)+c_{2}(x-a)^{2}+...+c_{n}(x-a)^{n}+...\]
anonymous
  • anonymous
:myininaya said this is this also true because everything is in the form of (x-n)^(n+1) starting with n=-1. doesn't that make it a power series? 7 minutes ago
anonymous
  • anonymous
You have (x-1)^2 and (x-2)^3 in the same series. 1 and 2 are not the same number, so this series is not centered around a point. That number being subtracted from x cannot change.
anonymous
  • anonymous
okay ty
myininaya
  • myininaya
ok nkili sounds right to me

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