已知1/6=1/2-1/3,1/12=1/3-1/4,1/20=1/4-1/5，那么1/6+1/12+1/20+1/30+1/42+1/56=？
已知1/6=1/2-1/3,1/12=1/3-1/4,1/20=1/4-1/5，那么1/6+1/12+1/20+1/30+1/42+1/56=？
1/6+1/12+1/20+1/30+1/42+1/56
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/2-1/8
=3/8
根据1/6=1/2-1/3,1/12=1/3-1/4,1/20=1/4-1/5...计算：1/6+1/12+1/20+1/30+......+1/90
1/6+1/12+1/20+1/30+......+1/90
=1/2-1/3+1/3-1/4……+1/9-1/10
=1/2-1/10
=2/5
1/6=1/2-1/3，1/12=1/3-1/4，1/20=1/4-1/5，根据以上规律计算下题。1/6+1/12+1/20+1/30+1/42+1/56+1/72
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/2-1/3+1/3-1/4+1/4-1/5+.....+1/8-1/9
=1/2-1/9
=9/18-2/18
=7/18
根据1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20…计算1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90的值。急！
∵1/2-1/3=1/6,1/3-1/4=1/12,1/4-1/5=1/20
∴1/5-1/6=1/30,1/6-1/7=1/42,1/7-1/8=1/56，1/8-1/9=1/72,1/9-1/10=1/90
将上述式子相加就行。
左边=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1/2-1/10
=2/5
右边=1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
∴1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=2/5
已知:1/2+1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,1/20=1/4-1/5. 求1/2+1/6+1/12+1/20的结果。
1/2=1-1/2,
1/6=1/2-1/3,
1/12=1/3-1/4,
1/20=1/4-1/5.
1/2+1/6+1/12+1/20
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.
=1-1/5
=4/5
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2/3-1/25= 观察1/6=1/2-1/3 ,1/12=1/3-1/4, 1/20=1/4-1/5...你能很快计算1/6+1/12+1/20+1/30+1/42吗？
1/6+1/12+1/20+1/30+1/42=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)=1/2-1/7=5/14
1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4… 根据规律计算这个： 1/6+1/12+1/20+1/30+1/42+1/56+1/72 5/6=1/2+
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18
1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7
=1-1/7
=6/7
已知1/2=1-1/2，1/6=1/2-1/3,1/12=1/3-1/4。计算1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90=？
1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+.....+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12 请你用发现的结 1/2+1/6+1/12+1/20+1/30+1/42+1/26
1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12 请你用发现的结
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8
=1-1/8
=7/8;
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已知:1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,求1/2+1/6+1/12+1/20+1/30.
解答：
1／2＋1／6＋1／12＋1／20＋1／30
=1－1／2＋1／2－1／3＋1／3－1／4＋1／4－1／5＋1／5－1／6
=1－1／6
=5／6
