1/6+1/12+1/20+1/30+1/42简便计算：2/3+2/15+2/35+2/63+2/991 1 1 1 1—--+—--+—---+——--+——--1*4 4*7 7*10 10*13 13*16 加上面一题,

1/6+1/12+1/20+1/30+1/42简便计算：2/3+2/15+2/35+2/63+2/991 1 1 1 1—--+—--+—---+——--+——--1*4 4*7 7*10 10*13 13*16 加上面一题,
1/6+1/12+1/20+1/30+1/42
简便计算：2/3+2/15+2/35+2/63+2/99
1 1 1 1 1
—--+—--+—---+——--+——--
1*4 4*7 7*10 10*13 13*16
加上面一题,

1/6+1/12+1/20+1/30+1/42简便计算：2/3+2/15+2/35+2/63+2/991 1 1 1 1—--+—--+—---+——--+——--1*4 4*7 7*10 10*13 13*16 加上面一题,

土豆团邵文潮为您答疑解难.
如果本题有什么不明白可以追问,

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

2/3+2/15+2/35+2/63+2/99
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11
=1-1/11
=10/11

原式=1/3*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3 *15/16
=5/16

您好：

1/6+1/12+1/20+1/30+1/42
=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7
=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

2/3+2/15+2/35+2/63+2/99
=2/1x3+2/3x5+2/5x7+2/...

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您好：

1/6+1/12+1/20+1/30+1/42
=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7
=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

2/3+2/15+2/35+2/63+2/99
=2/1x3+2/3x5+2/5x7+2/7x9+2/9x11
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11
=1-1/11
=10/11

第三题
原式=1/3x(3/1x4+3/4x7+3/7x10+3/10x13+3/13x16)
=1/3x(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3x(1-1/16)
=5/16





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如果有其他问题请采纳本题后另发点击向我求助，答题不易，请谅解，谢谢。
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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
=7/14-2/14
=5/14
2/3+2/15+2/35+2/63+2/99
=2×【1/（1×3)+1/（3×5）+1/（5×7）+1/（7×9）+1/（9×11）】
=2×（1—1/3＋1...

全部展开

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
=7/14-2/14
=5/14
2/3+2/15+2/35+2/63+2/99
=2×【1/（1×3)+1/（3×5）+1/（5×7）+1/（7×9）+1/（9×11）】
=2×（1—1/3＋1/3—1/5＋1/5—1/7＋1/7—1/9＋1/9＋1/11）×1/2……括号里正负抵消
=1—1/11
=10/11

1/1x4+1/4x7+1/7x10+1/10x13+1/13X16
=(1/3) × [ (1-1/4) + (1/4-1/7) + (1/7-1/10) + (1/10-1/13) + (1/13-1/16) ]
=(1/3) × [ 1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16 ]
=(1/3) × [ 1-1/16 ]
=(1/3) × (15/16)
=5/16

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望采纳！