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Question: Strange result for sum of binomials

Question:Strange result for sum of binomials

huguesmeyer 5 Maple
sum convergence binomial
September 28 2017
1

Dear Maple users,

I recently had to deal with the following sum :

sum(binomial(k+i,k),i=0..infinity)

for an arbitrary positive value of k. This sum obviously seems to diverge but Maple gives me 0 as a result for it. It looks very strange to me, but it might be the same sort of result as the sum of all the positive integers is -1/12. I am wondering whether the result Maple gives me is correct, and if yes, where does it come from ?

Any idea ?

Thanks a lot!
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