calculus II
posted by Harold on .
(A) 2 students are sharing a loaf of bread. Student A eats half of the loaf, then student B eats half of what remains, then student A eats half of what remains, and so on. How much of the loaf will each student eat?
(B) 2 students are sharing a loaf of bread. Student A eats 2/3 of the loaf, then student B eats half of what remains, then student A eats 2/3 of what remains, then student B eats half of what remains, and so on. How much of the loaf will each student eat?
(3) 3 students decide to share a loaf of bread. Student A eats half of the loaf, passes what remains to student B who eats half, and then onto student C who eats half, and then back to student A who eats half, and so on. How much of the loaf will each student eat?

make 2 columns, marked A and B
A eats 1/2 leaving 1/2  B eats 1/4 leaving 1/4
A eats 1/8 th leaving 1/8th  B eats 1/16 th, leaving 1/16 th
So A eats 1/2 + 1/8 + 1/32 + ...
a Geometric series with a=1/2, r = 1/4
S∞ = a/(1r) = (1/2)/(1  1/4)
= (1/2)/(3/4) = 2/3
So A eats 2/3 of the loaf
The clearly B must eat the missing parts or 1/3.
Do the others the same way. 
All I need to know is how do you do part two (2)? Is there a summation formula that we can use?

(4/9)^(n.5)