1x1/3+1/2x1/4+1/3x1/5....+1/19x1/21用简便方法计算等于多少
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解决时间 2021-03-15 08:31
- 提问者网友：世勋超人
- 2021-03-14 23:55
1x1/3+1/2x1/4+1/3x1/5....+1/19x1/21用简便方法计算等于多少
最佳答案
- 五星知识达人网友：酒安江南
- 2021-03-15 00:23
1x1/3+1/2x1/4+1/3x1/5....+1/19x1/21
=1/2x(1-1/3+1/2-1/4+1/3-1/5+……+1/19-1/21)
=1/2x(1+1/2-1/20-1/21)
=1/2x589/420
=589/840
=1/2x(1-1/3+1/2-1/4+1/3-1/5+……+1/19-1/21)
=1/2x(1+1/2-1/20-1/21)
=1/2x589/420
=589/840
全部回答
- 1楼网友：一袍清酒付
- 2021-03-15 01:32
原式=1/2 *（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+....1/18-1/20+1/19-1/21）=1/2* （1+1/2-1/20-1/21）
=589/840
=589/840
- 2楼网友：枭雄戏美人
- 2021-03-15 01:10
解：
1x1/3+1/2x1/4+1/3x1/5....+1/19x1/21
1x1/3+1/3x1/5....+1/19x1/21+1/2x1/4
=1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/19-1/21)+1/2x1/4
=1/2×(1-1/3+1/3-1/5+……+1/19-1/21)+1/8
=1/2×(1-1/21)+1/8
=10/21+1/8
通分就行了，不知道你这个+1/2x1/4是不是多写了
1x1/3+1/2x1/4+1/3x1/5....+1/19x1/21
1x1/3+1/3x1/5....+1/19x1/21+1/2x1/4
=1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/19-1/21)+1/2x1/4
=1/2×(1-1/3+1/3-1/5+……+1/19-1/21)+1/8
=1/2×(1-1/21)+1/8
=10/21+1/8
通分就行了，不知道你这个+1/2x1/4是不是多写了
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