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Goruby, 38 bytes ->n{dw{$.+=1;$..mp{1.0/-~_1}.su<n};$.} This was not as much fun as I thought it would be, but it was fun enough to use once.
Answer
Goruby, 38 bytes ->n{dw{$.+=1;$..mp{1.0/-~_1}.su<n};$.} This was not as much fun as I thought it would be, but it was fun enough to use once.