Question

a goat will eat 1/2 the grass of the field within 12 months, how much the time will take by the goat to finish all the grass ?

Answer 1

the goat will die first

Answer 2

grass grows

Answer 3

hi

Answer 4

\[\lim_{t \rightarrow ∞} \sum_{n=1}^{{t}} (1/2)^{n} = \lim_{t \rightarrow ∞}1=1\]

this equation says that even as time becomes infinite the process of eating half each time will never finish

Answer 5

hi,
However in a real world the grass could grow heaps slow and the field could be small, the goat would eat half, then half again reducing the field dramatically each year, the goat would get down to two grass plants left, then eventually two leaves of grass, i reckon he/she would eat both in such a case, which would be ok

Answer 6

unk has given us the answer to Zeno's paradox, but that only makes sense if you specify that the goat eats half of the REMAINING field every 12 months and ignore all the practical issues like grass growing and whatnot. I'd say the question is poorly phrased.