Three students share a bread. The first eats half, the second eats half of what is left, and the third eats half of that and so on....How much does each eat?
The fractions consumed by each
1 are 1/2 , 1/16 1/128 totalling ˝[1+(1/8) + (1/8)2 +…]
2 are 1/4 , 1/32, 1/256 totalling 1/4[1+(1/8) + (1/8)2 +…]
3 are 1/8, 1/64 1/512, totalling 1/8[1+(1/8) + (1/8)2 +…]
[1+(1/8) + (1/8)2 +…] = 1 / (1-1/8) = (8/7). Therefore,
1 consumes (1/2) (8/7) = 4/7
2 consumes (1/4) (8/7) = 2/7
3 consumes (1/8) (8/7) = 1/7
Note 4/7 + 2/7 + 1/7 = 1