2011 minus half of it, then minus the remaining 1 / 3, then minus the remaining 1 / 4, and so on, until finally minus the remaining 1 / 2011 Find the last remaining number

2011 minus half of it, then minus the remaining 1 / 3, then minus the remaining 1 / 4, and so on, until finally minus the remaining 1 / 2011 Find the last remaining number

From the meaning of the title
2011*(1-1/2)*(1-1/3)*(1-1/4)*.*(1-1/2010)*(1-1/2011)
=2011*1/2*2/3*3/4*.*2010/2011
(the denominator of the preceding number and the numerator of the following number can be omitted)
=2011*1/2011
=1