Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 2 / 14B / c

Solution

Write

D = f [x_{0}, \dots, x_{n}]

and let

D_{i}

x_{i}

omitted. By symmetry from part (a), reorder the full list so that its first node is

x_{i}

and its last is

x_{j}

. The recurrence from part (b) then has first omitted-node term

D_{i}

and second omitted-node term

D_{j}

, and gives

D = \frac{D _{i} - D _{j}}{x _{j} - x _{i}} .

This proves the requested identity for every pair

i \neq = j

There are no discussions about this article yet.

There are currently no matching articles.