1、5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+……+19x20/12

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1、5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+……+19x20/12
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1、5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+……+19x20/12
1、5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+……+19x20/1
2

1、5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+……+19x20/12
1、(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+……+(1/19-1/20)=1/5-1/20=3/20

0.15

1/30+1/42+1/56..........=(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+……+(1/19-1/20)=1/5-1/20=3/20

有规律可循：
1/5x6＝1/5-1/6
所以：本题答案是1/5-1/20=3/20

答案：3/20.
因为1/(5*6)=1/5-1/6
1/(6*7)=1/6-1/7
1/(7*8)=1/7-1/8
……
1/(19*20)=1/19-1/20
所以=1/5-1/6+1/6-1/7+1/7-1/8+......+1/19-1/20=1/5-1/20=3/20.

问题是这样吧...
1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+……+1/19x20
=(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+……+(1/19-1/20)
=1/5-1/20
=3/20

用裂项公式：1/n(n+1)=1/n-1/(n+1)
原式=(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+....+(1/19-1/20)=1/5-1/20=3/20

(1/5-1/6)+(1/6-1/7)+(1/8-1/9)......(1/19-1/20)
=1/5-1/20
=3/20

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