Therefore:1/3 =1/2× (1-1/3),1/3×1/5 =1/(3× 5
……
Therefore:1/3+1/(3× 5)+1(5× 7)+1(7× 9)+...1(1)
= 1/2×( 1- 1/3)+ 1/2×( 1/3- 1/5)+ 1/2×( 1/5- 1/7)+ 1/2×( 1/7- 1/ 9)+…+ 1/2×( 1/ 19- 1/2 1)
= 1/2×( 1- 1/3+ 1/3- 1/5+ 1/5- 1/7+ 1/7- 1/9+……+ 1/ 19- 1/2 1)
= 1/2×( 1- 1/2 1)
= 10/2 1