Question: Strange result for sum of binomials

Dear Maple users,

I recently had to deal with the following sum :


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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