Let f(x) be a polynomial of degree 2n for some natural number n such that f(x)=1/x for x=1,2,3,...2n+1. What is the value of f(2n+3)?

(In reply to

Thoughts by Brian Smith)

I quickly put together this program in ubasic to compute the final summation formula from my last post.

10 for N=0 to 99

15 Sum=0

20 for K=1 to (2*N+1)

25 Term=combi(2*N+1,K)*(2*N+2)/(2*N+3-K)

30 if (K@2)=0 then Sum=Sum-Term else Sum=Sum+Term

35 next K

40 print Sum;

45 next N

When ran it calculates a result of 1.0 for all N. So it would seem that f(2n+3)=1 for all functions f(x) as described in the problem.