求分数序列1/2,2/3,3/前20项和
时间: 2023-11-05 21:27:14 浏览: 92
首先列出前20项:
1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12, 12/13, 13/14, 14/15, 15/16, 16/17, 17/18, 18/19, 19/20, 20/21
然后求和,可以使用通分的方法:
1/2 + 2/3 + 3/4 + 4/5 + 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11 + 11/12 + 12/13 + 13/14 + 14/15 + 15/16 + 16/17 + 17/18 + 18/19 + 19/20 + 20/21
= (21/42) + (28/42) + (33/42) + (36/42) + (35/42) + (42/49) + (35/40) + (32/36) + (27/30) + (20/22) + (11/13) + (12/13) + (13/14) + (14/15) + (15/16) + (16/17) + (17/18) + (18/19) + (19/20) + (20/21)
= 1 + (2/3) + (3/4) + (4/5) + (5/6) + (6/7) + (7/8) + (8/9) + (9/10) + (10/11) + (11/12) + (12/13) + (13/14) + (14/15) + (15/16) + (16/17) + (17/18) + (18/19) + (19/20) + (20/21)
≈ 3.5976
因此,前20项的和约为3.5976。