Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?

A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand.

M children (1 to M) are standing in a circle facing each other wearing different caps. In the first round each passes his cap to the child on his left. In the next round each one passes the cap he now has to the second child on his left. In the next round each one passes the cap he has to the third child on his left and so on. They stop when the first child gets his original cap back for the first time.