Question

4/1*3+4/3*5+4/5*7+.+4/19*20=

Answer 1

你这道题分母没规律啊

应该是这样吧

4/1*3+4/3*5+4/5*7+.+4/19*21

=4[1/1*3+1/3*5+1/5*7+……+1/19*21]

=4[1/2(1-1/3)+1/2(1/3-1/5)+……+1/2(1/19-1/21)]

=2[1-1/3+1/3-1/5+……+1/9-1/21]

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

=2(1-1/21)

=2×(20/21)

=40/21