The expected number of trials needed to collect a complete set of 
different objects when picked at random with repetition is
(Havil 2003, p. 131). For 
, 2, ..., the first few values are
therefore 1, 3, 11/2, 25/3, 137/12, 147/10, 363/20, ... (OEIS A096617
and A027611).
Complete Set
Explore with Wolfram|Alpha
References
Havil, J. "Collecting a Complete Set." §13.9 in Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, pp. 130-131, 2003.Sloane, N. J. A. Sequences A027611 and A096617 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Complete SetCite this as:
Weisstein, Eric W. "Complete Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CompleteSet.html