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Follow the function (Posted on 2019-11-28) Difficulty: 3 of 5
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)?

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts re: Thoughts | Comment 3 of 6 |
(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.

  Posted by Brian Smith on 2019-12-08 01:06:42
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