Okay, time for another Problem of the Week! This little cutie is something I discovered by accident, while doodling around with iterated antiderivatives (but never mind which ones for now!):

Compute $\displaystyle \sum_{k = 0}^\infty \frac1{\binom{n+k}{k}}$ for $n > 1$.

Please send your solutions to topological[dot]musings[At]gmail[dot]com by Tuesday, June 3 (11:59pm UTC); do not submit solutions in Comments. Everyone who submits a correct solution gets mentioned in our Hall of Fame! Have fun…