duplicates merging I think that Determine sum of the series $\sum_{k=1}^\infty\frac{1}{n(n+1)(n+2)}$ is incorrectly closed as a duplicate of a question which is about a finite sum rather then about series.

But rather then reopening and finding a correct duplicate, it would probably be simple to merge it with: Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$.

One of the reasons why I think merging would be useful is that the question which is a "duplicate target" does not have answer using Gamma and Beta function, so Jack D'Aurizio's answer would add something new.

This question (and specifically the answer mentioned above) was discussed a bit here:

And since we are already on this question - should these comment be cleaned up? Are they just noise, or do documenting history how the questions were merged is worth keeping?

[ SmokeDetector | MS ] Offensive answer detected: Prove that $n+1 \\choose k$ = $n \\choose k$ + $n \\choose k-1$ by pozo's student on math.stackexchange.com