Difference between revisions of "User talk:PaoloMartini"
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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 | ||
= \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] | ||
− | = \sum_{i=0}^n \sum_{k=0}^i (-1)^k a_i {n \choose k} x^k.</math> | + | = \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 a_k {n \choose i} x^i (-1)^i.</math> | ||
+ | |||
+ | QED. | ||
---- | ---- |
Revision as of 18:14, 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.