how do we know if this is a power series 1+x+(x-1)^2+(x-2)^3+(x-3)^4+...

Question

how do we know if this is a  power series 1+x+(x-1)^2+(x-2)^3+(x-3)^4+...

anonymous · Answer

Since this is not centered around a point (you are subtracting different values from x each time), it is not a power series.

myininaya · Answer

because everything is in the form of (x-n)^(n+1) starting with n=-1.
doesn't that make it a power series?

myininaya · Answer

http://en.wikipedia.org/wiki/Power_series says it is

anonymous · Answer

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 · Answer

: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 · Answer

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 · Answer

okay ty

myininaya · Answer

ok nkili sounds right to me