Question

急急急急，快，数学题

1/1*3+1/3*5+1/5*7+...+1/17*19=？

Answer 1

1/1*3+1/3*5+1/5*7+...+1/17*19

=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/17-1/19)
=1/2(1-1/19)
=1/2(18/19)
=9/19

追问

能解释一下吗

追答

∵1-1/3=3/3-1/3=2/3
∴1/1*3=1/2×(1-1/3)
同理1/3*5=1/2×(1/3-1/5)
而1-1/3+1/3-1/5+1/5-1/7+……+1/17-1/19

中除首尾两项外-1/3+1/3、-1/5+1/5、-1/7+1/7……-1/17+1/17每组的和都为0
所以就剩下=1/2(1-1/19)
=1/2(18/19)
=9/19

Answer 2

(1-1/3+1/3-1/5+1/5-1/7+-----+1/17-1/19)÷2=（1-1/19）÷2=9/19

Answer 3

原式=1/2(1-1/3+1/3-1/5+1/5-1/7+......+1/17-1/19)
=1/2乘18/19
=9/19