Question

[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)

Answer 1

[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]

=(1+2010)*(2010/2)/((1005/1006)(1006/1007)...(2008/2009)(2009/2010))

=2011*(2010/2)/(1005/2010)

=2011*2010

=4042110