In this video, the interviewer asks "If I were to enter into a calculator, 1 plus 2 plus 3 plus 4 and so on out to infinity, and then hit equals, would I get the answer minus 1 twelfth?" The answer is of course, what does it means to do that "out to infinity?"
An interesting alternative valid question is, "If I were to enter -1 into a calculator, and then hit the zeta function button, would I get the answer -1/12?" The answer is, what kind of calculator provides the zeta function? The zeta function is a little bit more complicated to compute than, say, sine, but not too bad. It's not considered useful enough to provide, though perhaps if it were, it would stimulate more interest in analytic number theory.