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CTK Exchange
ke_45
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May-10-08, 11:09 AM (EST) |
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"Deriving functions based on differences"
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Hi If I had the following: f(n+1) - f(n) = (2·n - 1)² ...what techniques would I use to figure out the "f"? Don't solve, only suggest, please.
KE
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alexb
Charter Member
2224 posts |
May-10-08, 12:47 PM (EST) |
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3. "RE: Deriving functions based on differences"
In response to message #0
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The process is similar to finding an antiderivative. The "derivative" is a polynomial of degree 2. So you should be looking for an "antiderivative" as a polynomial of degree 3. So assume f(n) = an3 + bn2 + cn + d. Substitute this f into your equation. This will lead to a system of linear equations in a, b, c. Obviously, d is arbitrary. |
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