Tale of a frog that jumps a fraction of what is left to cross the pond I recall from undergraduate courses in calculus and series analysis a tale of a frog that tries to jump a fraction (e.g. 1/2) of what is left for the frog to cross the pond. 
In the limit, the fraction of the pond the frog travels is:
$1/2 + 1/2(1/2) + 1/2 (1/4) + ...$
Does this tale have a name?  What about the series? 

As one of the contents mentions, this story shares most of its properties with Zeno's paradoxes.  It seems similar in its description to Douglas Hofstadter's explanation of Zeno's paradoxes in his book Gödel Escher Bach.
As the other answer says, mathematically it's a geometric series.
