on the Nth button press, 1/N gets added to the displayed sum. displaying the sum as a floating point number is acceptable but boring; better would be something geometric to visually depict 1/N and the running sum. is there a way to visually suggest that the sum is unbounded?
similarly, add 1/nthprime(N) for an even more slowly diverging sum: OEIS A016088. or, Nth button press computes and displays the primality or factorization of N, then adds 1/N only if N is prime.
make it public art so that many generations of people can contribute toward infinity. or virtual: "welcome, visitor #N! click here to contribute 1/N to the sum."
the digamma function can probably used to evaluate a large harmonic partial sum avoiding round-off error. how can one sum reciprocals of primes minimizing round-off error?
instead of a button, a knob that clicks. the partial sum can be decreased.
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