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所有问题
1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=
如题所述
举报该问题
其他回答
第1个回答 2008-03-29
1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100
=(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+...+(1/2)(1/98*99-1/99*100)
=(1/2)*(1/1*2-1/2*2+1/2*3-1/3*4+...+1/98*99-1/99*100)
=(1/2)*(1/2-1/9900)
=(1/2)*(4949/9900)
=4949/19800.本回答被提问者采纳
第2个回答 2008-03-29
题目应为:1/(1*2*3)+1/(2*3*4)+...+1/(98*99*100)
原式=1/2*(1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+...+1/(98*99)-1/(99*100))=4949/19800
相似回答
1/
1X2X3+1
/
2X3X4+1
/
3X4X5+
...+1/
98X99X100
(要过程)
答:
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
--+1/
98x99x100 =
(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+...+(1/2)(1/98*99-1/99*100)=(1/2)*(1/1*2-1/2*2+1/2*3-1/3*4+...+1/98*99-1/99*100)=(1/2)*(1/2-1/9900)=(1/2)*(4949/9900)=4949/19800.
1/
1x2x3+1
/
2x3x4
.1/
98x99x100
拜托了各位
答:
1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
.1/
98x99x100=
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/98*99-1/99*100] =1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/98*99-1/99*100] =1/2[1/2-1/99*100] =1/2*...
计算1\
1x2x3+1
\
2x3x4+1
\
3x4x5+
```+1\48x49x50注:(\)为分数线(x)为乘 ...
答:
1\1x2x3=2x(1\1x2-1\2x3),所以:1\
1x2x3+1
\
2x3x4+1
\
3x4x5+
```+1\48x49x50=2x(1\1x2-1\2x3)+2x(1\2x3-1\3x4)+```+2x(1\48x49-1\49x50)=2(1\2-1\49x50)=1-1\49x25
1/丨
1x
2ⅹ
3+1
/
2x3x4+
……+1/8ⅹ9x10=
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 ...
奥数碰碰车:计算:1/
4x5+1
/5x6+1/6x7+1/7x8...+1/39
x4
0
=
?
答:
1/4x5+1/5x6+1/6x7+1/7x8...+1/39x40 =1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+……+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/...
Sn
=1
/(
1x2x3
)
+1
/(
2x3x4
)+...+1/(n(n+1)(n+2))
答:
=(1/2)[1-1/2-1/(n+1)+1/(n+2)]=(n^2+3n)/[4(n+1)(n+2)]其他类似的题目比如:1/
1x2x3+1
/
2x3x4+1
/
3x4x5+
---+1/
98x99x100 =
(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+...+(1/2)(1/98*99-1/99*100)=(1/2)*(1/1*2-1/2*2+1/2*3-...
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