1/1X2+1/2X3+1/3X4+...1/19X20=？
答案:4 悬赏:0 手机版
解决时间 2021-01-24 21:38
- 提问者网友：藍了天白赴美
- 2021-01-23 23:46
1/1X2+1/2X3+1/3X4+...1/19X20=？
最佳答案
- 五星知识达人网友：鸽屿
- 2021-01-24 00:06
解:
1/[n(n+1)]=1/n-1/(n+1)
1/1x2+1/2x3+1/3x4+...+1/19x20
=1-1/2+1/2-1/3+1/3+1/4+...+1/19-1/20
=1-1/20=19/20
1/[n(n+1)]=1/n-1/(n+1)
1/1x2+1/2x3+1/3x4+...+1/19x20
=1-1/2+1/2-1/3+1/3+1/4+...+1/19-1/20
=1-1/20=19/20
全部回答
- 1楼网友：山君与见山
- 2021-01-24 04:45
1/1X2+1/2X3+1/3X4+...1/19X20=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20=1-1/20=19/20
- 2楼网友：梦中风几里
- 2021-01-24 03:08
19/20
1/1X2+1/2X3+1/3X4+...1/19X20
=1-1/2+1/2-1/3+1/3-1/4+......+1/17-1/18+1/18-1/19+1/19-1/20
=1-1/20
=19/20
1/1X2+1/2X3+1/3X4+...1/19X20
=1-1/2+1/2-1/3+1/3-1/4+......+1/17-1/18+1/18-1/19+1/19-1/20
=1-1/20
=19/20
- 3楼网友：独行浪子会拥风
- 2021-01-24 01:31
1/(n(n+1))=1/n-1/(n+1)
1/(1*2)+1/(2*3)+.....+1/(19*20)
=1-1/2+1/2-1/3+1/3-1/4+....+1/18-1/19+1/19-1/20
约掉相反的项：
=1-1/20=19/20
1/(1*2)+1/(2*3)+.....+1/(19*20)
=1-1/2+1/2-1/3+1/3-1/4+....+1/18-1/19+1/19-1/20
约掉相反的项：
=1-1/20=19/20
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