Question

若m-n/mn=1/n-1/m,根据这一规律,计算4/1*3 +4/3*5 +4/5*7 +……+4/19*21

Answer 1

4/1*3 +4/3*5 +4/5*7 +……+4/19*21

=2*(2/1*3+2/3/5+2/5*7+……+2/(19*21)

=2[（3-1）/1*3+(5-3)/3*5+(7-5)*5*7+……+[(21-19)/19/21]

=2*(1-1/3+1/3-1/5+1/5-1/7+……+1/19-1/21）

=2*(1-1/21)

=10/21