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1/2x3+1/3x4+1/4x5......+1/8x9+1/9x10

1/2x3+1/3x4+1/4x5......+1/8x9+1/9x10 =(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/8-1/9)+(1/9-1/10) =1/2-1/10 =2/5

1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10 =1-1/2+1/2-1/3+1/3-1/4+....+1/8-1/9+1/9-1/10 =1-1/10 =9/10

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10 =1-1/2+1/2-1/3+1/3-....-1/9+1/9-1/10 =1-1/10 =9/10

1x2/1+2x3/1+3x4/1+4x5/1+5x6/1+6x7/1+7x8/1+8x9/1+9x10/1 =1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 =(1-1/2)+(1/2-1/3)+……+(1/8-1/9)+(1/9-1/10) =1-1/10 =9/10

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+1/5+...1/11) 因为后面的那个是一个发散数列,好像没有求和公式,所以只能同分计算,当然可以把简单...

先求它们的倒数和,再把结果倒回来。

n=10 ,很好算得,得440。也许我的方法很麻烦,但是思路是很不错的,可以1x2 2x3 3x4 4x5 5x6 6x7 7x8 8x9 9x10 10x11 =2 6 12 20

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