Difference between revisions of "User talk:PaoloMartini"
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PaoloMartini (talk | contribs) |
PaoloMartini (talk | contribs) |
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:<math>p(x-1) = \sum_{i=0}^n a_i (x - 1)^i |
:<math>p(x-1) = \sum_{i=0}^n a_i (x - 1)^i |
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= \sum_{i=0}^n \left[ a_i \left( \sum_{k=0}^n {n \choose k} x^k (-1)^k \right) \right] |
= \sum_{i=0}^n \left[ a_i \left( \sum_{k=0}^n {n \choose k} x^k (-1)^k \right) \right] |
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− | = \sum_{i=0}^n \sum_{k=0}^i (-1)^k a_i {n \choose k} x^k |
+ | = \sum_{i=0}^n \sum_{k=0}^i (-1)^k a_i {n \choose k} x^k |
+ | = \sum_{i=0}^n \left( a_i x^i \sum_{k=0}^i (-1)^k {n \choose k} \right).</math> |
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− | |||
− | zZzZ... |
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+ | QED. |
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Revision as of 17:50, 14 September 2006
Show that if is a polynomial of degree , then is a polynomial of the same degree.
Definition of polynomial.
Binomial theorem.
Special case.
Binomial coefficient simmetry.
Hence:
QED.