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2/1x2x3+2/2x3x4+2/3x4x5+2/4x5x6+...+2/98x99x100=
怎么做?我们一张数学卷子上的,请各位高手帮忙解决!要简便过程,谢谢
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推荐答案 2009-02-02
解:原式=(1/1*2-1/2*3)+(1/2*3-1/3*4)+……(1/98*99-1/99*100)
=1/1*2-1/99*100
=49499/99000
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1
×2x3十
2x3x4+3x4x5
十
4x5x6
十5x6x7十6x7x8十7x8x9=?
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
1乘
2+2
乘
3+3
乘4+···+99乘
100=
?
答:
1X2 +2X3 +3X4 = (
1X2X3 +
2X3X3 +3X4X3) /3 = [ 1X2X3 +2X3X(4-1) +3X4X(5-2) ] /3 = [ 1X2X3 -1X2X3 +2X3X4 -
2X3X4 +3X4X5
] /3
=
3X4X5 /3 1X2 +2X3 +3X4
+4X5
= (1X2X3 +2X3X3
+3X
4X3 +4X5X3) /3 = [ 1X2X3 +2X3X(4-1) +3X4...
1x2x3+2x3x4+
...+48x49
x5
0帮个忙解下
答:
只剩首尾Sn=[n*(n+1)(n+2)(n+3)-0*1*2*3]/4=n*(n+1)(n+2)(n+3)/4 把n=48代入 S48=48*49*50*51/4=1499400
1x2x3+2x3x4+3x4x5+
...+10x11x12
答:
解:设第n项为an an=n(n+1)(n+2)=n^3+3n^2+2n 1×2×
3+2
×3×4+...+10×11×12 =(1^3+2^3+...+10^3)+3(1^
2+2
^2+...+10^2)+2(
1+2+
...+10)=[10(10+1)/2]^
2+3
×10×(10+1)(20+1)/6+2×10×11/2 =3025+1155+110 =4290 用到的公式:1^3+2^...
巧算:10/
9x
7/8
x6
/13)÷(
3
/13x16/7
x5
/18)
答:
1X2X
1/3+
2X3
X1/4
+3X4
X1/5
+4X5
X1/6
+5X6
X1/7+6X7X1/8+7X8X1/9+8X9X1/10+9X10X1/11求和? 因为an=n*(n-1)/n+1 所以每个数可以看成2/3+(1+2/4)+(2+2/5)+(
3+2
/6)...+(8+2/11)= 1
+2+
3...+8+2/3+2/4+2/5...+2/11=36+2*(1/3+1/4+1...
1x2+2x3+3x4+4x5
……
99x100=
?
答:
原式 =1/3(
1x2x3
)
+2x3+
...
+99x100 =
1/3(1x2x3)+1/3(3x2x3)+...+99x100 =1/3(
2x3x4
)
+3x4+
...+99x100 =1/3(2x3x4)+1/3(3x3x4)+...+99x100 =1/3(
3x4x5
)+...+99x100 ...=1/3(99x100x101)=333300
2/
1x2x3
十2/
2x3x4
十...十2/
98x99x100
答:
1/((n-1)*n)-1/(n*(n+1)=1/2-1/(2*3)+1/(2*3)-1/(3*4)+...
+1
/(98*99)-1/(99*100)=1/2-1/(99*100)=4949/9900
1x2x3+2x3x4+3x4x5+.+
n(n+1)(n+2) 等于多少. 1X2+2X3+3X4+...+n(n+...
答:
1+2+...+n=n(n+1)/2 1^2+2^2+…+n^2=n(n+1)(2n+1)/6 1^
3+2
^3+…+n^3=n^2 * (n+1)^2 / 4 明确这三个式子就好了.
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