巧算:1/1×3+ 1/3×5+ 1/5×7 + …… +1/17×19

巧算:1/1×3+ 1/3×5+ 1/5×7 + …… +1/17×19

1/(n×(n+2))=( 1/n-1/(n+2) )/2
原式=(1-1/3+1/3-1/5+1/5-……+1/19)/2
=20/19/2=10/19