1X2X3分之一+2X3X4分之一+.+48X49X50分之一等于几
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1X2X3分之一+2X3X4分之一+.+48X49X50分之一等于几
原式=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+……+1/2*(1/48*49-1/49*50)
=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/48*49-1/49*50)
=1/2*(1/1*2-1/49*50)
=306/1225
解.裂项法.
1/[n(n+1)(n+2)]=(1/2){1/[n)n+1)]-1/[(n+1)(n+2)]}
=(1/2)[1/n-1/(n+1)-1/(n+1)+1/(n+2)]
=(1/2)[1/n-2/(n+1)+1/(n+2)]
S=1/1x2x3+1/2x3x4+1/3x4x5+...+1x/n(n+1)(n+2)
=(1/2)[1/1...
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解.裂项法.
1/[n(n+1)(n+2)]=(1/2){1/[n)n+1)]-1/[(n+1)(n+2)]}
=(1/2)[1/n-1/(n+1)-1/(n+1)+1/(n+2)]
=(1/2)[1/n-2/(n+1)+1/(n+2)]
S=1/1x2x3+1/2x3x4+1/3x4x5+...+1x/n(n+1)(n+2)
=(1/2)[1/1-2/2+1/3+1/2-2/3+1/4+1/3-2/4+1/5+/4-2/5+1/6
+.....+1/n-2/(n+1)+1/(n+2)]
=(1/2)[1-1/2-1/(n+1)+1/(n+2)]
=(n^2+3n)/[4(n+1)(n+2)]
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1X2X3分之一+2X3X4分之一+.+48X49X50分之一等于几
1x2x3+2x3x4+...+nxx=?
1X2X3分之一+2X3X4分之一+.+48X49X50分之一等于几1X3X5分之四+3X5X7分之四+.+95X97X99分之四等于几?1X2X3X4分之一+2X3X4X5分之一+.+17X18X19X20分之一等于几?中间的省略号代表以此类推.如果满意的话可以的60
1/1x2x3+1/2x3x4+.+1/98x99x100 .
1/1X2X3+1/2X3x4+…+1/48X49X50
1X2X3+2X3X4+.+n(n+1)(n+2)
1x2x3+2x3x4+.+nx(n+1)(n+2)=?
1x2x3+2x3x4+.+n(n+1)(n+2)=?
求和1x2x3+2x3x4+...+n(n+1)(n+2)
1x2x3+2x3x4+…+n(n+1)
1x2x3+2x3x4+3x4x5+…+8x9x10
1x2x3+2x3x4+3x4x5+.+10x11x12
1x2x3+2x3x4+3x4x5+...+7x8x9=,
1x2X3+2x3X4+3x4X5+…+7X8X9=?
1x2x3 2x3x4 3x4x5 .10x11x12,怎么算
求和:1X2X3+2X3X4+3X4X5+...+98X99X100
计算1x2x3+2x3x4+…+48x49x50
1x2=1|3(1x2x3-0x1x2) 2x3=1|3(2x3x4-1x2x3) 3x4=1|3(3x4x5-2x3x4)由此推断1x2x3+2x3x4+3x4x5.7x8x9=?