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1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 等于多少?急急急!!!
如题所述
举报该问题
其他回答
第1个回答 2012-09-22
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10
=1-1/2-1/2(1-1/3)
+1/2-1/3-1/2(1/2-1/4)
+1/3-1/4-1/2(1/3-1/5)
+1/4-1/5-1/2(1/4-1/6)
+.........
+1/8-1/9-1/2(1/8-1/10)
=1-1/9-1/2(1+1/2-1/9-1/10)
=173/360
本回答被提问者和网友采纳
第2个回答 2012-09-22
答案是2/9,主要是运用拆项运算。
第3个回答 2012-09-22
原式=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+……+1/8×9-1/9×10)
=1/2×(1/1×2-1/9×10)
=11/45
相似回答
1/丨
1x
2ⅹ
3+1
/
2x3x4+
……+1/8ⅹ
9x10
=
答:
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/
4x5x6+
...+1/
8x9x10
=1-1/2-1/2(1-1/3)+1/2-1/3-1/2(1/2-1/4)+1/3-1/4-1/2(1/3-1/5)+1/4-1/5-1/2(1/4-1/6)
+.+1
/8-1/9-1/2(1/8-1/10)=1-1/9-1/2(1+1/2-1/9-1/10)=173/360 ...
1
×2x3十
2x3x4+3x4x5
十
4x5x6
十5x6x7十6x7x8十7
x8x
9=?
答:
3x4x5=1/4x (
3x4x5x6
-
2x3x4x5
)………7×8×9=1/4×(7×8×9×10-6×7×8×9)∴1×2×3+2×3×4+……+7×8×9=1/4×7×8×9×10=1260
1x2x3x4+1
=
5x5
,2x
3x4x5+1
=11x11,3x
4x5x6+1
=19x19.第5个式子是?
答:
4*5*6*7+1=29*29 望采纳
数学题 急用!!
答:
1.1×2×3×4+1=25 2×3×4×
5+1
=121 3×4×5×6+1=361 4×5×6×7+1=841 2.25=5*5 121=11*11 361=19*19 841=29*29 结果都是平方数 3.猜想:4个连续正整数的积与1的和,是一个平方数 设4个连续正整数为n,n+1,n+2,n+3 n(n+1)(n+2)(n+3)+1 =[n...
奥数碰碰车:计算:1/
4x5+1
/
5x6+1
/6x7+1/7x8...+1/39
x4
0=?
答:
…+1/39-1/40 =1/4-1/40 =9/40 1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
...+1/
8x9x10
=(1/1x2-1/2x3+1/2x3-1/3x4+1/3x4-1/
4x5+
...+1/8x9-1/9x10)÷2 =(1/1x2-1/9x10)÷2 =(1/2-1/90)÷2 =22/45÷2 =11/45 ...
请1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/
4x5x6
=
答:
=1/2×(1/1×2-1/2×
3+1
/2×3-1/3×
4+1
/3×4-1/4×
5+1
/4×5-1/5×6)=1/2×(1/1×2-1/5×6)=7/30
1X2X3X4+1
=25=5²
;2x3x4x5x6+1
=121=11²
;3x4x5
x6x7+1=361=19²...
答:
(n²+5n+5)²
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/
4x5x6+
...+1/
8x9x10
等于多少?急急急
!!!
答:
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/
4x5x6+
...+1/
8x9x10
=1-1/2-1/2(1-1/3)+1/2-1/3-1/2(1/2-1/4)+1/3-1/4-1/2(1/3-1/5)+1/4-1/5-1/2(1/4-1/6)+...+1/8-1/9-1/2(1/8-1/10)=1-1/9-1/2(
1+1
/2-1/9-1/10)=173/360 ...
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