An infinite crowd of mathematicians enters a bar. The first one orders a pint, the second one orders a half pint, the third one orders a quarter pint, and so on.
The bartender interrupts, "I get it!" – then pours the order for all of the mathematicians. How many pints does the bartender pour?
If the first three terms of a geometric progression are given to be find the sum to infinity of all of its terms.
If the answer is in the form of for positive integers and with square-free, find the minimum value of .