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Calculus/Frog crossing a bridge

Question
Hi Professor Mantell,

This is a problem that I recall from college although I don't remember how it all works out. I believe it is a calculus problem....or, at least, I hope so.

A frog is crossing a bridge and each time he hops, he hops half the distance left remaining in order to get over the bridge. So, if the bridge is 100 long, he hops 50 feet then 25 feet, and on and on. Does he ever get all the way across the bridge?

I'm guessing you're familiar with the 'problem' and can tell me how it works. Thank you for your help with this and also for being so generous with your time!

Woody

Hello Woody,

Yes, it is a familiar problem (or ones like it).

Theoretically, the frog never reaches the end of the bridge...since there will always be
some distance (however small) that remains...
50+25+12.5+6.25+3.125+... approaches 100, but never gets to it.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you, Dr. Mantell!

Calculus

Volunteer

Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook