Take half of a foot of space every day, then take 1/2 on the first day, and take half the next day, that is, (1/2) 2. . . .

Take (1/2) n on the nth day.

(1) Then, after the fifth day, the remaining1-[(1/2)+(1/2) 2+...+(1/2) 5] =/kloc-.

Time remaining on day 6: 1/64

Remaining after 10:11024

(2) 1-[( 1/2)+( 1/2)^2+...+( 1/2)^n]=( 1/2)^n

(3)( 1/2)^n<； 1/ 1000000

2^n>； 10 6, both sides take natural logarithm at the same time:

nln2 & gt6ln 10

n & gt6ln 10/LN2 = 19.93 16

n=20

After 20 days, there is less than a millionth of a foot left in a foot pestle.

Essentially, it is to investigate the summation of geometric series.