# CALC 2

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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?

C. 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?

• CALC 2 -

1 at start
a eats 2/3 ** 1/9 *** 1/54
b eats 1/6 ** 1/36 ** 1/108
first line is geometric series
2/3 + 2/3(1/6) + (2/3)(1/6)^2 ...
An = 2/3 +(1/6)^n-1
sum of that series = a/(1-r)
= (2/3)/(1-1/6) = 2/3 /5/6 = 4/5

• CALC 2 -

try similar for the rest

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