Consider this not-so-difficult sum:
It consists of just a string of fractions up to whichever N you happen to choose. Add them up, and you certainly and unambiguously have a number. If you chose to stop at N = 10, you'd find that f(10) = 1627/2520, which is about 0.645635. If you chose to stop at N = 100, you'd find f(100) = 0.692647. If you've taken calculus in college, you can show without…