infinite mathematicians enter a bar. the first orders a pint of beer, the second orders half a pint. the third orders a quarter pint, and the bartender cuts them off there and just pours them two pints
after a time the mathematicians indicate they're ready for another round. as before, the first one orders a pint and the second orders a half. when the third orders a third of a pint the bartender says "actually i think you've all had enough for tonight"
@typhlosion A great many sequences start in those ways. How does the bartender know after only three terms that the mathematicians are using those specific sequences?
Related: I wonder if 1 + 1/2 + 1/3 + 1/6 + 1/11 converges, with the denominator of each term equal to the sum of the previous three denominators.
Related: is there any scholarly work on the behavior of Fibonacci-like sequences where you add the previous n>2 numbers?
@DialMforMara maybe they've tried this before
@typhlosion I think the tribonacci numbers converge. My pen-and-paper math suggests the sum is close to 2.2
@typhlosion and the bartender learned that they did not have infinite patience