**S**ome sums and limits found from a [vacation] riddle by The Riddler:

*For the first method, Friend 1 takes half of the cake, Friend 2 takes a third of what remains, and so on. After infinitely many friends take their respective pieces, you get whatever is left.*

*For the second method, Friend 1 takes ½*^{²} of the cake, Friend 2 takes ⅓^{²} of what remains, and so on. After infinitely many friends take their respective pieces, you get whatever is left.

*For the third method, Friend 1 takes ½*^{²} of the cake, Friend 2 takes ¼² of what remains, Friend 3 takes ⅙² of what remains after Friend 2, and so on. After your infinitely many friends take their respective pieces, you get whatever is left.

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