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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+...

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  1. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    http://en.wikipedia.org/wiki/Power_series says it is

  4. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    :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
    • 5 years ago
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    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
    • 5 years ago
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    okay ty

  8. myininaya
    • 5 years ago
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    ok nkili sounds right to me

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