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