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所有问题
1/1x2x3+1/2x3x4+1/3x4x5+............+1/9x10x11=
如题所述
举报该问题
其他回答
第1个回答 2010-07-23
1/n(n+1)(n+2)=1/2*[1/n-2/(n+1)+1/(n+2)]
原式=1/2*(1-2*1/2+1/3+1/2-2*1/3+1/4+....+1/9-2*1/10+1/11)
=1/2*(1-1/2-1/10+1/11)=27/110本回答被提问者采纳
相似回答
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/4x5x6
+.+1
/8x
9x10
等于多少?急!
答:
请1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/4x5x6= =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 1/1x2x3+1/2x3x4+1/3x4x5+...+1/
9x10x11=
1/n(n+1)(n+2)=1/2*[1/n-2/(n+1)+1/(n+...
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+.+1
/8x
9x10
如何计算方法 详细步骤,谢谢_百度...
答:
则原式=(1/2)[1/(1×2)-1/(9×10)]=(1/2)[(1/2)-1/(90)]=11/45
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
...+1/8x
9x10
如何计算方法
答:
则原式=(1/2)[1/(1×2)-1/(9×10)]=(1/2)[(1/2)-1/(90)]=11/45
1/(
1x2x3
)
+1
/(
2x3x4
)+1/(
3x4x5
)+.
答:
将问题中的计算数字化如下:1/(
1x2x3
)+ 1/(
2x3x4
) +1/(
3x4x5
)
+
...+ x1/(98x99x100)由上述式子可以看出,第n项是1/[n(n+1)(n+2)],由1/[n(n+1)(n+2)]与1/n,1/(n+1),1/(n+2)的关系,可以知道下式成立:1/[n(n+1)(n+2)]=1/2x[1/n+1/(n+2)]-1/(n+...
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/4x5x6+...+1/8x
9x10
等于多少?急急急...
答:
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+1
/4x5x6+...+1/8x
9x10
=
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 ...
数学简便计算 1/
1x2x3+1
/
2x3x4+1
/
3x4x5
……+1/20x21x22=?
答:
1/1×2×3=1/2×(1/1×2-1/2×3)其他以此类推 所以原式=1/2×(1/1×2-1/2×
3+1
/2×3-1/3×4+……+1/20×21-1/21×22)=1/2×(1/1×2-1/21×22)=115/462
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
...+1/8x
9x10
求简算
答:
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
...+1/8x
9x10
=1
/2 [1/1×2-1/2×3+1/2×3-1/3×4+1/3×4-1/4×5+。。。+1/8×9-1/9×10]=1/2[1/2-1/90]=1/2×44/90 =11/45
1/
1x2x3+1
/
2x3x4+1
/
3x4x5
答:
解1/(1+2+3)+1/(2
+3+
4)+1/(3+4+5)……+1/(99+100+101)=1/6+1/9+1/12+1/15...
+1
/300 =1/3*(1/2+1/3...+1/99+1/100)=1/3*4.18737751763961 =1.39579250587987
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