1. ## Help me to solve it, please.

A giant rabbit is tied to a pole in the ground by an infinitely stretchy elastic cord attached to its tail. A hungry flea is on the pole watching the rabbit. The rabbit sees flea, jumps into the air and lands one kilometre from the pole (with its tail still attached to the pole by the elastic cord). The flea gives chase and leaps into the air landing on the stretched elastic cord one centimetre from the pole. The rabbit, seeing this, again leaps into the air and lands another kilometre away from the pole (i.e., a total of two kilometres from the pole). Undaunted, the flea bravely leaps into the air again, landing on the elastic cord one centimetre further along. Once again the rabbit jumps another kilometre and the flea jumps another centimetre along the cord. If this continues indefinitely, will the flea ever catch up to the rabbit? (Assume the earth is flat and extends infinitely far in all directions.)

2. ## Re: Help me to solve it, please.

flea on rabbit bugs bunny ?

3. ## Re: Help me to solve it, please.

If it is precalculus, this is a limit problem. The distance between them increases at each jump by 99,999 cm. So, after $n$ jumps, the distance between them is $99999n$ cm. Take the limit as $n$ approaches infinity. If it is zero, then the flea eventually catches up. If it is a positive number or if it approaches infinity, the flea never catches up.