## anonymous 5 years ago how do we know if this is a power series 1+x+(x-1)^2+(x-2)^3+(x-3)^4+...

1. anonymous

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

2. myininaya

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

3. myininaya
4. 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 $\sum_{n=0}^{\infty}c_{n}(x-a)^{n}=c_{0}+c_{1}(x-a)+c_{2}(x-a)^{2}+...+c_{n}(x-a)^{n}+...$

5. 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

6. 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.

7. anonymous

okay ty

8. myininaya

ok nkili sounds right to me