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## Homework Statement

a) Two friends, Jon and Bob, are sharing a loaf of bread. Jon eats half of the loaf, then Bob eats half of what remains, then Jon eats half of what remains and so on. How much of the loaf did each of them eat?

b)Jon is hungrier and eats 2/3 of the loaf, then Bob eats half of what remains, then Jon eats 2/3 of what remains, and Bob eats half of what remains and so on. How much of the loaf did each of them eat

c) Now there are Jon, Bob and Ron. Jon eats half of the loaf, then Bob eats half of the remains, and Ron eats half and so on. How much did each of them eat?

## Homework Equations

For geometric series:

[tex]\sum(c*r^n)[/tex] with n starting from 0 approaching infinity = c/(1-r), |r|<1

## The Attempt at a Solution

I made a table upto the fourth sum for all three parts, but I'm still confused on how to come up with a general series equation. Once I get the general solution, the sum should be easy i think.

for part a, i got for Bob--[tex]\sum(1/4)^n[/tex] where n=0 going to infinity. and for Jon im doubtful i got [tex]\sum1/2^n[/tex] where n=1 going to infinity. I dont know how to start for the other parts, don't see any obvious solutions.