1/3*5= 1/2( 1/3- 1/5)

..... and so on.

1/ 1*3 + 1/3*5 + 1/5*7 + 1/7*9....+ 1/ 17* 19

= 1/2 ( 1- 1/ 1/3- 1/5+ 1/5- 1/7+ ...

= 1/2( 1- 1/ 19)

=9/ 19

It is known that a=-2 b=- 1

1/a b+ 1/(a- 1)(b- 1)+ 1/(a-2)(b-2)..... 1/(a-20 12)(b-20 12)

= 1/ 1*2+ 1/2*3+ 1/3*4+....+ 1/20 13*20 14

= 1/ 1- 1/2+ 1/3+ 1/3- 1/4+ 1/2065438.

= 1- 1/20 14

=20 13/20 14