原式= 1 2 (1- 1 3 )+ 1 2 ( 1 3 - 1 5 )+…+ 1 2 ( 1 19 - 1 21 )= 1 2 (1- 1 3 + 1 3 - 1 5 +…+ 1 19 - 1 21 )= 1 2 (1- 1 21 )= 10 21 .故答案为: 10 21 .