# Difference between revisions of "User talk:PaoloMartini"

Jump to navigation
Jump to search

PaoloMartini (talk | contribs) |
PaoloMartini (talk | contribs) |
||

Line 23: | Line 23: | ||

:<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 |
+ | = \sum_{i=0}^n \sum_{k=0}^i a_i {n \choose k} x^k (-1)^k |

= \sum_{i=0}^n \sum_{k=0}^i a_k {n \choose i} x^i (-1)^i.</math> |
= \sum_{i=0}^n \sum_{k=0}^i a_k {n \choose i} x^i (-1)^i.</math> |
||

## Revision as of 18:16, 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.