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?

This looks like a geometric series, which is a series of the form

$$\sum_{n=0}^\infty a r^n$$

In your case $a = \frac{1}{2}$ and $r = \frac{1}{2}$.