Question

1/1×3+1/3×5+1/5×7+…1/17×19+1/19×21这道题如何简便运算?

Answer 1

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

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

=1/2*(1-1/21)

=10/21