Need help with a math riddle turned complicated

[OhDestnz]

So in school i was given a math riddle by a friend of mine (this is what we do for fun). He explained an answer to me but i didnt really get it. the riddle goes as: there is a rabbit with an infinitely extensible rope tied around it strung to a pole 1000 metres away. there is also a flea on the pole. the flea jumps one metre to get the rabbit on top of the rope. then the rabbit jumps 1000 metres to get away from the rope. will the flea ever get to the rabbit. we got to an answer with a very messy answer. we said yes because the flea gets closer to the rabbit by a factor of (n+1/n) (because when the flea has jumped one metre and the rabbit jumps 1000 metre the rope will stretch and that one metre turns into two meters and if you continue it increases by a factor of (n+1/n). So we had this answer but then said to each other how may times would the flea actually have to jump to get to the rabbit. so i went home and thought about it. i considered the rabbits jumping to be an arithmetic series and the flea to be a geometric series (im not too sure i can do that with the flea), i said that if i make two equations for the sum of both and equate them i can find out the value for how many times it jumps. so i tried this and got stuck. this is what i done. R represents the rabbit and F represents the flea.

R:
a=1000 d=1000
sn=n/2(2a+(n-1)d)
=n/2(1000n+1000)
=500n^2+500n

F: a=1 d=n+1/n
sn=(a(1-r))/(1-r)
i cant really write this out but i got to (n^n)/(n^-1)

This is where i got stuck. i equated them and i got to 1=n^n(500n+500)

Please could i have some help i would really appreciate if someone could check what i have done or even do it themselves and work out how many times the flea would have to jump. thanks in advance

 

[stapel]

There is a rabbit with an infinitely extensible rope tied around it strung to a pole 1000 metres away. There is also a flea on the pole. The flea jumps one metre to get the rabbit on top of the rope.

I don't understand the last statement. If the flea is at the pole and the rabbit is one kilometer away from the pole, how does the flea influence the rabbit by jumping one meter? What is meant by "getting the rabbit on top of the rope"? Thank you!

 

[stapel]

Is this puzzler maybe a version of the one outlined here?

 

[OhDestnz]

I don't understand the last statement. If the flea is at the pole and the rabbit is one kilometer away from the pole, how does the flea influence the rabbit by jumping one meter? What is meant by "getting the rabbit on top of the rope"? Thank you!

so the rabbit who is attatched to the pole with the string is 1000 metres away. the flea is on the pole. the flea is trying to get to the rabbit, so it jumps 1 metre. the rabbit responds by jumping 1000 metres. then the flea jumps again and the rabbit jumps again. this repeats as a cycle

 

[OhDestnz]

Is this puzzler maybe a version of the one outlined here?

this is really similar to the question thanks for this. However i have a question. it says on the ant problem that its a harmonic series that diverges to a specific value. wouldnt that mean you could work out the sum to infinity as the modulus of r(the difference) would be less than 1