Question

1×2×3分之1+ 2×3×4分之1+3×4×5分之1+4×5×6分之1，等于多少

Answer 1

1/1×2=1/2=1-1/2
1/2×3=1/6=1/2-1/3
1/3×4=1/12=1/3-1/4
.............
1/98×99=1/9702=1/98-1/99
规律1/n(n+1)=1/n-1/(n+1)
1/1×2+1/2×3+1/3×4+…+1/98×99
=1-1/2+1/2-1/3+1/3-1/4+...++1/98-1/99
=1+(-1/2+1/2)+(-1/3+1/3)-1/4+...+(-1/98+1/98)-1/99
=1-1/99
=98/99
是否可以解决您的问题？

Answer 2

1/1×2=1/2=1-1/2
1/2×3=1/6=1/2-1/3
1/3×4=1/12=1/3-1/4
.............
1/98×99=1/9702=1/98-1/99
规律1/n(n+1)=1/n-1/(n+1)
1/1×2+1/2×3+1/3×4+…+1/98×99
=1-1/2+1/2-1/3+1/3-1/4+...++1/98-1/99
=1+(-1/2+1/2)+(-1/3+1/3)-1/4+...+(-1/98+1/98)-1/99
=1-1/99
=98/99

Answer 3

1×2=1/2=1-1/21/2×3=1/6=1/2-1/31/3×4=1/12=1/3-1/4.............1/98×99=1/9702=1/98-1/99规律1/n(n+1)=1/n-1/(n+1)1/1×2+1/2×3+1/3×4+…+1/98×99=1-1/2+1/2-1/3+1/3-1/4+...++1/98-1/99=1+(-1/2+1/2)+(-1/3+1/3)-1/4+...+(-1/98+1/98)-1/99=1-1/99=98/99全文
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有爱872aTyLV.42014-07-12